On my 850 the glovebox light was staying on because the glovebox door had warped slightly and increased the clearance to the shutoff switch enough that the light never went off. This would kill the battery in 5-7 days, not overnight ... but I had a good battery.

I used epoxy to attach a nickel as a strike plate inside the glovebox cover where it hits the switch. This fix has been working great for four years now. I like to say that this in the only thing I fixed on my Volvo for only five cents!

open the front and rear doors. Trip the door latch mechanism so as to simulate the door latch striking the catch. This should extinguish the door courtesy lights on the rear of the door. Pull up the door handle to reset the latch before closing the door. They must be tested independently on my 96 850 because each latch controls only that door. Easy to remove bulb by prying out plastic lens. A lot cheaper than replacing door handle electrical component.

This would have been easier to fix last week, but now you have to wait an hour later for the sun to set.
When it is dark, if you have a sedan lower the rear seat back and check if the trunk light is on. Check the lights over the rear doors to make sure they all go off. Check the glove box light. If it is the glovebox light, glue a penney to the spot where the plastic switch touches the door.

Klaus
--
(V♂LV♂s 1975 164, 1995 854T, 1998 V70R)

I bought my car new and am only on the third battery--perfectly normal battery usage. You probably just have an aged battery.
--
96 850T, Bilstein HD, IPD swaybars

Check your glove compartment. Sometimes with 850's the glove box door is closed, but doesn't push the switch in to turn of the glove box door. If this doesn't do it, check the rear hatch (if wagon) for the same reason. Good luck!
--
1998 S70 T5 Emarald Green Metallic, 2004 V70 2.5T Ruby Red, Previous Owner of Black '94 850 Turbo Wagon. My cars have been running so well lately they've got me worried.