88 jaguar xj6 turns off, and sometimes on again all by itself

if it is the old type dash they suffer dry/bad solder joints on the printed circuit, if the later dash sounds like a bad ground on the lower a post i think rh or transmission tunnel rh

either the starter is not engaging all the way or there is a bad spot on the ring gear, remove the starter and turn the engine and check the ring gear if its good then look at the starter

electrical issue, bad bulb, burned bulb some item like that. Check side markers, turn signals, parking lights etc

Check the window switch itself. First turn the key in on position and listen if you hear the window motor clicking. If you hear the motor clicking the motor itself is bad. If you don't hear the clicking the switch itself is bad. If more than one window is affected, the window switch is bad. If your right signal just stays lit up, get out of the car while it's on, and see which bulb, the front or rear, is not on. The one that isn't on is the one that needs to be replaced.

Does check engine light or wrench light come on? If yes, get free computer scan from Autozone or other parts store that offers free scan. Sounds like a sensor is failing

Is the car immobilized? if so you may have to lock and unlock the car with the key and not the remote.

Is it turning over or just nothing, also starter motor may be jammed. put the car in gear with the hand brake off and push the car forward until you feel the engine turn over. You dont need the keys in the car!

This should free the starter off, sometimes they jam very tight and will not move at all, on these jags. they get rusty quickly if sat about. I had a XJ many years ago great motors.

Good luck.

this could be camshaft position sensor is most likely the cause

check for broken wire at the wheel hub sensors

the steering wheel lock doesnt lock in till the steering wheel is turned a bit .as for the dash lights and wipers i would need to play with it to sort this one out ,because it could be anything froma earth wire to ??

if you have the dash manual it will tell you how to restart it.i know gm cars you turn ignition switch to the on position for ten minutes engine not running.when security light turn off the engine will start up. but jaguar might be a different tactic.