2000 Jeep Cherokee has the part time 4WD light on while in 2WD mode. I’ve switched the unit into part time 4WD and the light gets brighter and when I shift back to 2WD mode the light goes completely out, but later it come back on. Solutions please?

Go under the vehicle and shift the transfer case into 2WD manually.
Does the light go out?
The linkage from the factory was clearly designed by an engineer on drugs!!
Bushings wear out, etc, etc.
If this solves the problem, then a new after market linkage from Boost Werks or Azzy would
be an easy fix.
If the light still stays on, then someone else with more electrical experience will have to chime in.
Mike

When your light is on in 2wd, turn sharply on dry road,...is it jerky/chirpy or jack up 1 front wheel...does it rotate freely? its very possible your shifter linkage has slipped and you are in 4wd. Or the wires to the 4wd sensor might be worn through the insulation and touching

There is also a sensor in the transfer case that controls when the light is on or off. It has a detent on the tip that can get gunked up or rusted and locks up. They are cheap and easy to replace, usually less than 15 bucks.