I spent the weekend cleaning out the attic and while I was up there I figured I should check out what caused the old water stain on the ceiling of the nursery closet. A few extra trips up and down the ladder and I placed the stain directly below the AC drip tray/overflow pan.
After checking that there were no holes in the tray, I'm calling this to-do item done. We had the unit professionally inspected and adjusted this year and there were no major problems and as much as I'm in the attic, I've never seen a drop of water in the tray. I'm guessing the stain is from an older HVAC unit that has since been replaced.
That's the thing about inspector's list for older homes - sometimes the problem is already fixed, only the proof that it once existed is still there.