Happened before, but not as such:

92 Cherokee Limited
162k

Headlights, on the way home, began randomly shutting off and on.
I started toggling the brights on and off, which would help for a sec, and then the lights would go off.
However, when I would toggle it on/off at times, the bright light on the dash would remain on, yet the lights were in normal mode.
I would hit the brights again, the brights light would go off, and so would my lights.

Pulled over, pulled in/out, fiddled with the switch, and it didn't do it again.

Would the switch cause the light to remain on on the dash?
I'm starting on a reground this week as soon as I pick up the stuff.
Brand new headlights (ultravision - two weeks ago).
Brand new battery as of today.

 

and would it be the headlight switch or the dimmer switch?

 

from your description, the re-grounding seems to be a clear first choice. I am sure you are aware that all the power for your headlights runs thru the switch, which is not the best of plans. Are the headlight plugs corroded? wire insulation brittle/exposed wires? There is much written here dealing with a variety of headlight woes... look around you will find someone has had this issue. Consider a harness/relay upgrade while your at it. You will not be disappointed.

 

The Ultravision headlights are a higher wattage than stock. The stock headlight switch and wiring are not made for the extra power as all the power for the lights go through the switch. The best thing that you can do is to upgrade the wiring harness for the headlights and put them on relays. You can either buy a kit or make your own, that's what I did.