Several questions have already been asked on 1 Samuel 28 (e.g. here, here & here), but none has had a focus on what Saul believed about Sheol. In 1 Samuel 28, the witch of En-dor describes Samuel as coming up out of the earth (upwards), meaning that the spirit of Samuel had to have been somewhere downwards, which--judging by Saul's reaction--made perfect sense to his worldview:
11 And the woman saith, `Whom do I bring up to thee?' and he saith, `Samuel -- bring up to me.' 12 And the woman seeth Samuel, and crieth with a loud voice, and the woman speaketh unto Saul, saying, `Why hast thou deceived me -- and thou Saul?' 13 And the king saith to her, `Do not fear; for what hast thou seen?' and the woman saith unto Saul, `Gods I have seen coming up out of the earth.' 14 And he saith to her, `What [is] his form?' and she saith, `An aged man is coming up, and he [is] covered with an upper robe;' and Saul knoweth that he [is] Samuel, and boweth -- face to thee earth -- and doth obeisance.
[1 Samuel 18:11-14 YLT]
If Saul had strongly believed that the spirit of Samuel was somewhere else (e.g. in heaven, which would be upwards -- see Psalm 11:4, 1 Kings 22:19, Isaiah 63:15), then the words of the witch describing Samuel as "coming up out of the earth" wouldn't have made sense to Saul. Therefore, it should stand to reason that Saul's worldview included as part of its beliefs that the spirits of the dead were somewhere downwards. But where exactly?
The first place that comes to my mind is Sheol. According to JewishEncyclopedia:
It connotes the place where those that had died were believed to be congregated [...]
Sheol is underneath the earth.
Unfortunately, the word Sheol is not found anywhere in 1 Samuel 28. However, 1 Samuel 2:6 does mention it:
Jehovah putteth to death, and keepeth alive, He bringeth down to Sheol, and bringeth up.
Similarly, David, a contemporary of Saul, alluded to Sheol and the condition of the dead multiple times (see Psalm 6:4-5, 16:10, 30:9, 88:10-12, 115:17, etc.). He explicitly mentioned Sheol a few times:
4 Turn back, O Jehovah, draw out my soul, Save me for Thy kindness' sake. 5 For there is not in death Thy memorial, In Sheol, who doth give thanks to Thee?
[Psalm 6:4-5 YLT]
10 For Thou dost not leave my soul to Sheol, Nor givest thy saintly one to see corruption.
[Psalm 16:10 YLT]
According to Wikipedia, the reign of Saul is traditionally placed in the late 11th century BCE. Some centuries later, Isaiah--who is believed to have lived in the 8th century BCE (source)--referred to Sheol in terms that would match the apparent worldview of Saul:
9 Sheol beneath hath been troubled at thee, To meet thy coming in, It is waking up for thee Rephaim, All chiefs ones of earth, It hath raised up from their thrones All kings of nations. 10 All of them answer and say unto thee, Even thou hast become weak like us! Unto us thou hast become like! 11 Brought down to Sheol hath been thine excellency, The noise of thy psaltery, Under thee spread out hath been the worm, Yea, covering thee is the worm.
[Isaiah 14:9-11 YLT]
The Book of Numbers, whose final form was probably consolidated in the 5th century BCE (source), recounts an incident in chapter 16 about people who went down to Sheol alive:
30 and if a strange thing Jehovah do, and the ground hath opened her mouth and swallowed them, and all that they have, and they have gone down alive to Sheol -- then ye have known that these men have despised Jehovah.' 31 And it cometh to pass at his finishing speaking all these words, that the ground which [is] under them cleaveth, 32 and the earth openeth her mouth, and swalloweth them, and their houses, and all the men who [are] for Korah, and all the goods, 33 and they go down, they, and all that they have, alive to Sheol, and the earth closeth over them, and they perish from the midst of the assembly;
[Numbers 16:30-33 YLT]
Lastly, during the 1st century AD, Luke the Evangelist recorded Jesus' parable of Lazarus & the rich man (Luke 16:19-31), which was based on Pharisaic doctrines on Hades (the Greek word for Sheol), including the existence of a compartment for the righteous known as the Bosom of Abraham:
22 `And it came to pass, that the poor man died, and that he was carried away by the messengers to the bosom of Abraham -- and the rich man also died, and was buried; 23 and in the hades having lifted up his eyes, being in torments, he doth see Abraham afar off, and Lazarus in his bosom,
[Luke 16:22-23 YLT]
Note: I'm mentioning dates and citing multiple sources to bring awareness into the broad historical context surrounding the Jewish concept of Sheol.
Would Saul, an Israelite King from the 11th century BCE, have believed that the spirit of Samuel (and the spirits of the dead in general) was in Sheol?
Was that the predominant view at the time (11th century BCE)?
Can a historical and cultural analysis shed light on the answer?
(*) Note that a similar question could be asked about Isaiah (8th century BCE).