Patching and Plastering - corner drywall tape problem

Have a sky light, up in the box that was finished with drywall and then painted probably ten years ago has evidence that two areas of the drywall tape (inside corners) apparently where not covered with enough drywall compound (if you got up in the box and looked you could almost see the tape line) and the tape came loose. I have carefully lifed it and worked Elmers Contractor glue and it seems fine now but I am wondering if I can still put a thin skin of drywall compound on the area, prime it and get it ready for the finish coat (the ceilings are going to be repainted? Or should I just leave the repaired area alone and repaint as is?

I'd add a coat of joint compound if it needs it. That will also let you know if the glue is holding. Normally wet j/c is used to reglue the tape but I suppose elmers would work - just never tried it.

Often the skylight 'holes' don't get painted as well as they should. That may have contributed to the j/c and tape failure. Between the heat from sunlight and condensation, that drywall needs to be primed and painted as well as the walls you can reach should be.

I'd check the attic side of the skylight for insulation and a vapor barrier. Any moisture in the house escaping into the attic could be working it's way back to the hot (solar energy) chase and wetting the tape enough to cause it to lift. I see this alot around skylights, near the top. I would pull it out after cutting the bad section and mud a new piece in, not glue.
Be safe, Gary