2001 Sequoia, door ajar light goes off, but dome light stays on. Door ajar light comes on with slight pressure against closed door. Can replacing the door jam switch solve this problem? Why would the door ajar light and door and under dash courtesy lights go off, but dome light stays on?

Check for corroded wire connector kick pad driver side clean wire try this or change the connector

replace the relay for the door ajar switch
it is a notorious faulty relay that goes bad with all Ford built vehicles

i must say that i feel your pain with this,, my door ajar light does the same thing but my dome light doesn't come on when the doors are open, i have to flick the switch on the dome light to make it come on. In my opion and i stress my opion it saounds like a issue with the body controller, im not sure what ford calls it but it controls all the body functions, i dont think the low coolant light is connected to the body contoller but i dont know this for sure, i think that light is controlled bny the engine ecm. some times a dealer can connect to the body controller and see if there are any fault codes for circuits that it controls and or monitors, also they can reflash or update the configeration and or calibration level cause ford release's fixes for issues all the time, same theory works for any control module on a vehicle. i dont think any of the auto parts stores have the right program to connect to bofy controlers but i could be wrong, worth looking into. i only put up with mine cause i use it as a beater, if you are worried about your dome light staying on and drianing your battery then you could pull out or disconnect the dome lights for the time being, its not a fix but just a band-aid.

in the door jam there is a switch it sounds like the switch either needs to be adjusted or replaced to adjust loosen the big flat screw at the bottom and turn the switch to acheive the right height. if it is at the correct height then try a new switch. this should solve that problem if not then you have me stumped also.

sounds like thats your problem,the drivers door is the one that goes bad the most,switch is located in door latch.youll have to remove door panel,and maybe latch,call a ford dealer and ask if you could buy just the switch or do you have to replace latch asm.

The door sensors will need to be replaced. A screws can be removed and then a wire can be taken of and you then can replace the switch.

There is a magnet type sensor in the door jamb and door that come together when you close the doors.You have to replace the magnet switch in the door that it is bad in. these newer model Fords are notorious for those particular switches going bad

The drivers side door switch goes bad all the time on those, try replacing or check if its sticking.the small little button int the door jam.

On the 01 Lincoln it has something to do with the keyless pad on the door press and hold button 9-0 till the green light around it goes out!

I know the problem. Mine does it too. The fix is easy. Open & close doors to find which one is causing the problem. Open that door panel and find the release latch at back of door. There are 2 wire harnesses attached to the latch. Unhook the wires and spray sockets of latch. There is a ballbearing that gets stuck in switch. Lubricate that ballbearing and work latch manually several times. This problem will reoccur occasionally especially when there has been a lot of rain. Good Luck