My 2003 Escape 2.0L has the "door ajar" light on the dash permanently lit, including with the engine off and key removed, which means that I have to switch the courtesy light on and off by hand or else it stays on.

Obvious first guess is a fault with a door or tailgate switch, but they all look OK to a visual inspection. Are there any multimeter tests I can do? Any specific voltages/resistances to look for?

 

Out back glass often leaves the light on. Try closing it very firmly.
As far as testing the switches, I'm not even sure where they are but they should either be open or closed - 12v or nothing.