Welcome to TRS
Two different issues
Does the "door ajar" light come on when drivers door is open?
There is a switch in each door on the latch mechanism that is connected to the GEM, generic electronic module.
The GEM is what controls the dome light(and door ajar light) and wipers, power windows and pretty much anything electrical in the cab, including the Chime.
So when you open the drivers door the GEM should get that signal and turn on the dome light, its not.
Most likely the door switch is the problem, drivers door gets used the most.
Generally this switch gets stuck in the open position so door ajar light stays on all the time
Google: Ford Ranger Door ajar light
GEM has the Chime built in, small piezo "speaker" that can be replaced if you have soldering skills
If this is a new truck to you then the chime may have been disabled, many do NOT like it, lol.
How it was disabled would be the question if thats the case
GEM is behind the radio and not to hard to get at, just remove the trim and unscrew radio, you could test wire to drivers door and the chime at the same time
read this thread:
https://www.ranger-forums.com/inter...3/how-disable-door-chime-2000-rangers-104559/