I read through rather quickly, have you determined that the hole in the tube is on the inner (rim) side, or on the outer (rolling) side? Someone mentioned using a cotton ball, this is my favorite trick for something that's embedded in the tire but that you can't see. A cotton ball will snag and leave a trail of cotton right back to the culprit. If it's on the inside, I would entirely remove any and all rim tape and re-install new tape carefully and evenly. There are many youtube videos on how to do this correctly. Part of doing it correctly is dependent on having the correct width of tape. It should fit from rim sidewall to rim sidewall with no gaps. It is worth trying the cotton ball trick on the rim as well. If there is a little burr that is causing your issues, again the cotton will snag on the offending burr.

If the tube doesn't seem to have a hole, the next thing I'd check is the valve core. If it's dirty, or not entirely screwed in (if it's a removeable core) then air will slowly seep out of the valve.