1993 grand cherokeeoverdrive button light stays on ,no overdrive

Having a professional hook up a scan tool an check codes would tell you ,

wow no engine size stated, the 5.2L run a special trans... so....
hopeless to help you much.
zj jeep with automatic.
it didnt lie, it told you to service it, so take it to a shop and let the work on this old dog..
stuck , now what does that mean.
the shift lever lever stuck, or its cable failing end to end.? or?
or shifts from 1 to 2 and hangs there.
or down shifts from 3 to 2 and and hangs there
DIY ? question is that it? you never said intentions.....
so we open the 93 ZJ book and what do we see.
ax-15 stick box, seems not.
the aw-4 auto , electronically shifted with TSM (scan it yet?)
and the 46RH auto. used on the 5.2L, has no TCM brain.
its a Hydramatic.
here are the OD words off the 46h page

Overdrive Control Switch
The overdrive control switch is located in the instrument
panel. In the On position, automatic shifts
into fourth gear overdrive will occur. In the Off position,
the switch overrides the powertrain control module
preventing a shift to overdrive fourth gear range.
The switch has an indicator light that illuminates
when overdrive is turned off. The switch also resets
when the ignition key is turned to the OFF position
so that the automatic overdrive feature is restored.
The use of fault codes is employed to help diagnose
the electronic components that operate the overdrive
unit and torque converter clutch.

I'm not sure your best bet but I had a 91 accord and I lef't O/D on all the time and just didn't work the engine like crazy all the time.

this is a common issue on these cars and since you just had the trans replaced, whoever did the work needs to check the connections at the switch and at the trans-and these switched go bad, but the fact that it was just done to too much of a coincidence.

your "overdrive" button has been pushed and overdrive has been turned off. The switch is at the end of your gearshift lever, simply press the button and the light should turn off.

The light illuminates to tell you that the overdrive is off, that is why your engine RPM's go up. When the light is on, the overdrive is off.

This is a tough one! Lets start with the easiest first, When was the tranny fluid changed last? Have you checked the level? Maybe low on fluid? It almost sounds like maybe you have a contaminated fluid. I would start by checking the fluid level and the fluid condition. If the fluid is low then add some if it looks funny or smells burnt I would flush the system and change the fluid and go from there. I hope this helps you.

see where the wiers from overdrive go and fix there a switch. all it is a switch. or just connect the wiers together to turn the overdrive off

its vapor locking try leaving the fuel cap a little lose!!!!

hi first of all check the temp sensor on the auto box.also check transmission oil cooler that it is not blocked.when the computer for the auto box detects a problem it turns off the over drive.