I use Zap and Crazy Glue brands because that's what my local stores carry.
I initially removed the excess glue after I installed my screw eyes, but now I leave it to act as a seat, to prevent "unscrewing"
I also run the eyes in until the bottom of the eye make a small divot in the bait, that's filled by the excess glue.
I haven't had an eye unscrew since I stated doing that.
For bigger baits, like swimbaits, that have enough weight to provide leverage as a fish thrashes, I use Spro swivels for my hook hangers. The wire will break before the swivel comes out of the tight hole I drill. I seat those swivels in Crazy Glue, too.