More thoughts on the dome light/aux delay relay, operation. On my 99, the aux delay relay, sometimes called the power window relay, is time out operated by the GEM to provide power to the windows for about a minute after shutting the engine down, as long as we don't open a door. This allows us to power an open window up, if we forgot before turning the engine off.
Apparently this relay is also used to power & turn the overhead/dome lights off after about a minute after exiting the vehicle, depending on how the vehicle is equipped. In any case the GEM controls this accessory relay, that switches power to a number of things depending on how the vehicle is equipped. SO, if Dr Ken doesn't find dome light relay joy in the Aux Relay Box, look to the delay relay clipped to the tang under the glove box door.
Pushing the passenger side seat all the way back & laying on our back in the passenger side foot well & looking up, we'll see it clip mounted left/right on that metal tang under the glove box door.

Give that puppy a thump & see if the dome light will time out & turn off with the doors closed. If it won't, the relay contacts may be welded, so remove the relay, take it out of its plastic housing & clean its contact points with a new clean dollar bill, see sawed back & forth between the contacts, to clean & polish them up & see if that'll wake it up. Or just replace that puppy, but be prepared for sticker shock, which is why I cleaned & reused mine!!!!