96 jeep jeep cherokee cruise the light come on but as soon as you take off the light go out

JEEP what? wrangler, cherokee, GC, what?
early cruise, (add on major parts on new car, under hood.)
and is a very serious matter.
i think , open hood, see cruise box(actuator) disconnect it from
the throttle body (TB what is that?) get it serviced now.
the free book is here, read both cruise chapter,
the 2nd in in wiring. see how to unplug the electics.
if that fails, the first chapter shows the actuator and how to disconnect the LINKage. to end its control safey forever.
http://www.jeep4x4center.com/knowledge-base/index.htm?utm_source=cj#service

lots of jeeps, pick one

It sounds like you either have an Electrical Issue with the PCM or your Band is slipping and you are looking at a rebuild sometime soon.

Also check brake switch adjustment, it is the interrupter.

There is a fuse layout in the owner's manual... and on the fuse box lid.

Are you certain it is #20 - and not a 20A fuse?

It is either 15A (blue) or 20A (yellow)

Without a diagram - you can verify all of them quite easily with a simple $4 test lamp from the parts store.

With the key in the ON position test for voltage at both sides of each fuse.
Whichever fuse does not light on both tabs is a bad fuse.
You could have them all tested in 2 minutes.

Thanks!!

crank shaft sensor, as soon as car warms up, it will skip (engine stutter(, then when engine cools, so does crank shaft sensor. Good Luck

Check the vacuum hoses it is easy to notice if one is missing or not. If that doesn't work, I'd try the cruise control switch. Hope this helps

I press the control switch on my 1999 Jeep cherokee. the cruise light doesn't come on and the cruise does not engage. Please offer a solution.

take to auto sparky-sounds like solenoid

Check fuses/relays and make sure they are all good; if so check the electrical wiring/connectors in the dash. Jeeps are notorious for loose wires in the dash.