what dtermines whether an ineligible player sits out or JUCO?

No one knows, but believed to be a factor:

Relative prestige of school vs. ranking of recruit
Money spent on recruit
Random die roll

don't think money spent is a factor.  a while back (rails - i believe) spent over $60k on a recruit that went juco.  last season in smith DII, i spent $10,330 on a kid that went juco (that is slightly over 2 scholarships worth of DII money). 

If you are having a hard time determining on whether or not to go after an ineligible, just ask yourself:  1) Can I get the player and 2) can I wait a season on him?  If you can't wait a season for a player, then don't go after them and waste your money on a chance that he might not show up.

I think it's 100% random, I don't see any correlation between prestige, recruit rank and effort put in. In the recruiting that just ended in Tark I signed an ineligible who was ranked in the 130s for PGs all I did was 10 scouting trips and he showed up with my B- prestige. The season before I signed an ineligible who was ranked in the 150s for Cs and I did 10 scouting trips and 20 HVs with a B+ prestige and he went to JUCO.