When the Kingdom of Israel split, what happened to Benjamin?

Question

All my life I've been told that the tribe of Benjamin remained with the faithful tribe of Judah. And I've read the passage in 1 Kings 11:29-35 where the kingdom is split in two many times before, but never noticed this before today.

31 Then he told Jeroboam, “Take ten pieces, for this is what the Lord God of Israel says: ‘Look, I am about to tear the kingdom from Solomon’s hand and I will give ten tribes to you. 11:32 He will retain one tribe, for my servant David’s sake and for the sake of Jerusalem, the city I have chosen out of all the tribes of Israel. (1 Kings 11:31, 32)

Ten tribes go to Jeroboam. One tribe remains with the descendant of David (for David's sake). The passage repeats several times these numbers.

(I note that the numbers also only add up to 11. I am inferring that the tribe of Levi was out of the question here as they had not inherited a division of land upon entry. They were to serve throughout the area.)

Why has Benjamin been so often said to remain with Judah? Where did this tradition come from?

Answer 1

In 1 Kings 12:20, it is written, "...there was none who followed the house of David except the tribe of Yehuda only." Regarding this phrase, Rabbi David Kimchi (RaDaK) wrote,

כבר כתבנו כי שבט בנימין בכלל שבט יהודה, כי ירושלם בין שניהם היתה ומי שימלוך בירושלם בודאי ימלוך על שניהם, לפיכך נכלל שבט בנימין בכלל שבט יהודה

which is translated as,

We have already written [that phrase] since the tribe of Binyamin ("Benjamin") was among the tribe of Yehuda ("Judah"), for Yerushalaim ("Jerusalem") was between the two of them. And whoever reigned as king in Yerushalaim definitely reigned over both of them. Therefore, the tribe of Binyamin is included with the tribe of Yehuda.

Shortly after 1 Kings 12:20 wherein it is written that only the tribe of Yehuda followed the house of David (i.e., the dynasty of kings descended from David), we find mention of the tribe of Binyamin in 1 Kings 12:21, 

And when Rechav'am came to Yerushalaim, he assembled all the house of Yehuda, with the tribe of Binyamin, a 180,000 chosen men, who were warriors, to fight against the house of Yisra'el, to bring the kingdom again to Rechav'am, the son of Shlomo.