I have a 92 4.0L with a puzzling headlight issue.
When the engine is running, my low headlamps flicker, that is, they turn off and on with no dimming and no pattern. This happens after driving for 15-20 minutes.
When I switch to high beams, there are no problems.
No effect on stop/turn/parking/etc.

 

You should check your headlight switch and connector. All the power goes through the switch and they can get fried easily, especially if you've put better bulbs in as they draw more power. You might just need to clean the connection but you should look at an upgrade. Replace the stock harness on the headlights and add relays so that a minimum about of power goes through the switch. Even just upgrading the harness will make your lights brighter. It's a lousy design.

 

I just replaced the headlight switch last night. It now lets me turn on the dome lights, but no fix on the headlights.

 

Check and clean grounds. Check connections and wiring.

 

Click on the link in my signature and go to post 3.

 

Exactly the same problem with mine, New headlight switch 1-2 years ago worked fine - now keeps kicking in and out - Ive taken a video here ( you can hear the lights clicking in and out towards the end from inside the cabin) going to look into what you guys have already suggested.