I've posted about this before. Headlights go off and on by themselves. Changed headlight switch. Battery is new (dead cell, not for headlights). Negative cable seems fine. Is there not a relay in this circuit?

think there is fuse link on driver side inner fender well that acts up and makes the head lights do this.

Did you change the switch with a new one or one from a pick a part?

Once the first switch heats up and burns, you may find that the matching plug on the harness has been burned also. Plugging a burned harness plug onto a new switch will again cause a loose connection that generates heat. And the cycle repeats, headlights blink and another switch burns up. Check the plug. Another problem with these (as happened on my '90 Dakota) was the headlight lead wire burned at the bulkhead connector where the circuit passes through the firewall (Driver side near where the steering column passes through). Pull the cover and you'll find a green corroded connector. I pulled wire straight through the bulkhead and spliced the wires direct without connectors and sealed it back up with silicone, permanent fix.

New. Connector looked fine.

What I've done;

New battery (installed BEFORE lights starting blinking)
Alt 13.9 while running
Bypassed dimmer switch
Replaced headlight switch/connector looked good
Replaced headlights
Checked firewall main harness connector
Checked ground (all other lights are fine)
Shook and wiggled every wire on the vehicle
Links on driver inner fender look intact, do not get hot, not melted and do nothing when wiggled
Ground strap could be replaced, but all the other lights are fine

I know electrical can be a nightmare, but this is nuts.

if you have power in the red wire, try jumping it to the headlight wire itself, at the switch. (remove the switch, and jump the wires) it's entirely possible to buy a brand new, piece of junk switch, that doesn't work. if you start at the hot wire at the switch, and work your way forward with the headlight wires, you'll find the problem quickly. there's nothing extra in the way of this, except for passing through the bulkhead.

i replaced my switch back in january, for the same problem. advance gave me a bad switch. vato-zone gave me a good one.

Can I just bypass this wiring with a relay type kit?

You'll still need a good source of power to operate the relay from the switch. Do you have a DVOM?

Yes

The switches have contacts in them with bimetal strips that will open up when they get too hot, like a circuit breaker. You either have a bad switch or excessive resistance in the circuit somewhere. Find your battery wire to the switch and connect the voltmeter to it with the connector plugged in. Connect the other end to the hot wire at the headlamp, turn the headlights on, you should be reading around 0.1 volt. If it's more than that you have excessive resistance in the circuit. Turn the lamps off, disconnect the head lights and switch and start probing backwards, measuring the resistance to outside and inside of bulkhead and back to the switch. It should be less than 0.2 ohms. If it is measure the resistance of the ground circuits from the headlamp connector to the body ground and back to the battery to find out where the excessive resistance is. If all this fails to find anything go get another switch.

SOB! It was the new headlight switch. Chinese junk! Made the auto store swap it for another piece of crap until I can find a Mopar switch. Anyway, I appreciate all the help. At least I know all the other wiring is good to go!