One has to do a bit of detective work to figure this conundrum out. Before reading this answer, I would recommend that you read Michael Heiser's short article, from the second subheading "Who Killed Goliath?", because we have a similar manuscript situation on our hands.
The first question we need to ask is:
How did The Apostle Paul know about the length of Saul's reign?
Credit goes to Paul Knauber for spotting this first part. In his paper on Judges Period Chronology he states the following:
“In an attempt to unmuddle these waters, I searched the Scriptures for other clues. The first such clue is provided in 2Sam 2:10a:
Ishbosheth, Saul’s son, was forty years old when he began to reign over Israel, and he reigned two years. Only the house of Judah
followed David [NKJV]
Turning back to 1Sa 13:1-2, you can see the further problem this presents. If Saul is 30 or even 40 when he becomes king and reigns
only 2 years, Ish-Bosheth could not be 40 when Sauldies. Both 1Sa 9:2
and Josephus, in his Antiquities, describe Saul at the time of his
anointing as a “young man,” which expression is somewhat nebulous.
Even if the Apostle Paul is right about Saul reigning 40 years,
Ish-Bosheth’s age of 40 at Saul’s death is possible, but unlikely, if
Saul is crowned as a Truly young man. With every attempt to resolve
the chronology of this period, I could not do so with Saul as a young
man at his coronation. But as the word “young” is comparative, and
relative to some reference: it is not determinant. That is, a man of
40 years might, to some, be considered a young man. Not only do we
have Ish-Bosheth at 40 when Saul dies, but we have his son Jonathan
joining him in battle against the Philistines (1Sam 13:2) immediately
after his confirmation as king (1Sam 11:12-15). Does a man 30 years
old have a son old enough to be a soldier? Possible, but unlikely. It
is far more likely that Saul was 40 when crowned. Note that as soon as
this engagement with the Philistines is complete,1 Sam 14:49 says,
The sons of Saul were: Jonathan, Jishui, and Malchishua. And the names of his twodaughters were these: the name of the firstborn Merab,
and the name of the younger Michal. [NKJV]
Ish-Bosheth is not named here, so is presumably yet to be born. If he is born immediately thereafter, then his age of 40 at Saul’s death
would coincide directly with Saul’s reign. Thus,the figure of 40 years
for both Saul’s age at his coronation, and the term of his reign are
virtually inescapable.”
We get confirmation of this by looking at the end in 1 Samuel 31:2 where we find:
“The Phi·lisʹtines kept in close range of Saul and his sons, and the Phi·lisʹtines struck down Jonʹa·than, A·binʹa·dab, and Malʹchi-shuʹa,
Saul’s sons.”
Only Three out of Four sons are mentioned yet again. We have one different name, Abinadab instead of Jishui (or Ishvi according to some translations). Could it be that Ishvi is Ishbosheth? This is unlikely as Ishbosheth already has an alternative name, Eshbaal (1 Chronicles 8:33, 9:39). It is unlikely that Ishbosheth had a third name. I find it more likely that Ishvi’s alternative name was Abinadab. Ishvi means “He resembles me”, whereas Abinadab means “my father is noble” or “father of a vow”, which could be a name change to reflect his fathers change in state to a noble king, or it could be related to the events surrounding Saul’s rash vow early in his reign.
The point is, Ishbosheth wasn't born yet, inferring at least a 40 year reign of Saul, corroborating Paul’s 40 years reference in the book of Acts. This is bigger than Paul realizes, as it helps fully explain the 1 Samuel 13:1 conundrum.
The Similarity of 1 Samuel 13:1 and 2 Samuel 2:10
Seeing both 1 Samuel 13:1 and 2 Samuel 2:10 in quick succession, something immediately jumps out at you. Both have references to 2 years, with Saul mentioned in both verses with an age reference at the start of reigning. This prompted me to compare, the Hebrew for 1 Samuel 13:1 and 2 Samuel 2:10 to see if there were any other correlations:
You’ll notice that every word in 1 Samuel 13:1 is identical to the words that make up 2 Samuel 2:10 with identical spelling. The only difference is that 4 words & 1 Letter have been dropped, and two words have been moved to the end of the sentence. Is it possible that 2 Samuel 2:10 has been interpolated into 1 Samuel 13:1? How could this come about?
Scribal Interpolation Hypothesis
Suppose for a moment that other scribes and teachers also realized you could use 2 Samuel 2:10 to figure out Saul's reign length (just like Paul). They conclude Saul must have reigned for at least forty years. Now the scribes/ teachers see in their scrolls that every single King of Israel except Saul has a reign length associated with them. An example of this can be seen at 2 Kings 18:2:
“He was 25 years old when he became king, and he reigned for 29 years
in Jerusalem.”
We find these types of passages at the start of the account of each King, this is the established pattern. The scribe/ teachers then think it would be a good idea (for completeness) to add in a similar verse for Saul, using the information from 2 Samuel 2:10. They task a copyist to add something like "And For Forty Years, Saul Reigned Over Israel" into the text just before 1 Samuel 13:2 (Right after he is confirmed King), using the information from 2 Samuel 2:10.
Now these scrolls take weeks/ months for a copyist to produce, longer if they are doing multiple books. By the time the copyist gets to 1 Samuel 13, he has either forgotten exactly what the task was, or wasn't paying attention properly to understand what the significant/ relevant information from 2 Samuel 2:10 required was. But he remembers at the very least that he needs to go to 2 Samuel 2:10. He takes a stab at the task anyway (sometimes people do this to save the embarrassment of asking again and then having to explain why they forgot to make any notes of the task in the first place, this sort of thing happens frequently in the world of Architecture if you forget a clients requirements). Instead of cherry picking the relevant information like he was tasked with, He ends up copying a large portion of 2 Samuel 2:10 into 1 Samuel 13:1. But instead of reading "Ish-boʹsheth, Saul’s son, was 40 years old when he became king over Israel, and he reigned for two years." (2 Samuel 2:10) as it reads in its original place, the interpolation reads "Saul was 40 years old when he became king over Israel, and he reigned for two years." The copyist has removed everything about Ishbosheth. That’s only Three less Hebrew Words, like so:
We now have this variant finding its way into circulation. We now have two versions of 1 Samuel 13, one containing 13:1, and the other original not containing it. The Dead Sea Scrolls community receives the variant & notices that this verse is near identical to 2 Samuel 2:10, but because Saul is more prominent than Ishbosheth, and because the Saul narrative comes first, they remove 2 Samuel 2:10 from their manuscripts, believing that verse to be the error (this is why the verse is absent from the dead sea Scrolls). I predict that the absence of 2 Samuel 2:10 in the Dead Sea Scrolls would point to 1 Samuel 13:1 being present with a reading of “forty years”. Unfortunately, this chapter is not present in the dead sea scrolls at all to verify.
Second Textual Change
In another community that has received the variant, a copyist comes along to this corrupted text. Not knowing precisely what mistake the first copyist has made, this copyist tries to "fix" this error and makes the problem worse (like with the Michael Heiser Goliath’s brother case). Firstly, the copyist notices that "there is no way Saul reigned for only 2 years, (1 Samuel 27:7 David spends 1 year and 4 months in Philistine territory), there is no way 1 Samuel 13-27 occur in an 8 month period." Then he thinks he knows what mistake was made, but just makes it worse as follows:
He imagines that the error is that the text wasn't originally a regnal length text (like 2 Kings 18:8), and that it was actually just a time skip text. He has already made it a few letters into the verse before he notices this error, and he doesn't want to have to start a new scroll from scratch because that is weeks of work down the drain. So, he removes the word for "Forty" (trying to remove association with King Reign texts).
Next, he wants to change the way the "two years" are applied. In order to do this, he will need to rearrange the order of the sentence and alter the "and two" into "and when two years". He removes a single letter from the end of "two years", turning it from a complete regnal length statement into a passive "when 2 years"; a time skip statement. Then he moves 2 words from the middle of the sentence to the back of the sentence for grammatical correctness. This text now resembles how the modern corrupted 1 Samuel 13:1 text appears.
Continuity Coherence.
How do we know that it was 2 Samuel 2:10 copied into 1 Samuel 13:1 and not the other way around? If we were to assume that 1 Samuel 13:1 was the original, we then have the many variations we see today, each one presenting narrative problems (Either Saul being Thirty or a Two-year reign creates continuity errors. There would also be no clear motive to fabricate information about Ishbosheth, copying it from Saul). If on the other hand, 2 Samuel 2:10 was the original, the narrative of 1 Samuel 8-15 makes more sense with 1 Samuel 13:1 absent. The Garrison/ oppression of the Philstines mentioned in 1 Samuel 9:16, 10:5, 13:3 is dealt with more immediately, and the 330,000 Israelites originally gathered (1 Samuel 11:8) most of which are sent back to their tents (1 Samuel 13:2) and are then called back into the battle after the 3,000 succeed (1 Samuel 13:4) aren’t sat around doing nothing for two whole years (if this was indeed a time skip verse). So assuming that 1 Samuel 13:1 was the original, either a 2 year time skip, or a 2 year total reign for Saul creates problems. With the other way around as I am proposing, there are no continuity errors. No Time skip for Saul works better, and a 2 year regnal length for Ishbosheth is problem free in its own narrative.
You can turn 2 Samuel 2:10 into 1 Samuel 13:1 by removing 4 Hebrew words and 1 letter, and by moving two words from the middle to the end of the sentence. The textual variance family tree for all of the above would look as follows:
Conclusion
In the original Hebrew, every single word present in 1 Samuel 13:1 is present also in 2 Samuel 2:10. The spellings are identical. It is highly unlikely that two verses dealing with the same/ similar subject matter would use all the exact same words in a near identical order with no variation in spelling (Just compare 1 Samuel 14:49 and 1 Samuel 31:2 and you’ll see what I mean). The evidence would indicate that the words from 2 Samuel 2:10 were copied into 1 Samuel 13:1.
I think it is now safe to conclude that 1 Samuel 13:1 is an interpolation into the text from 2 Samuel 2:10 made by well-meaning scribes and a mistaken execution of their idea. This means then that the Greek Septuagint version where this verse is omitted preserves the original reading of the text.
It also shows that we already possessed all of information needed to resolve this issue, but simply nobody made the connection. The answers were there all along.
Interlinear Of 2 Samuel 2:10
Interlinear Of 1 Samuel 13:1
Information On 1 Samuel 13:1 Variants