71 Duster Headlight issues

You have an area in the system with high resistance. If the lights are shutting off, it's likely tripping the breaker inside you headlight switch.

Yes it will do it both on high and low beam. Usually on high beam it starts screwing up sooner. I definitely think it something heating up. Look at and cleaned the firewall connection not that it needed it. I’m thinking either high/low beam switch or the headlight on off switch especially if it has some sort of breaker or relay built into it.

The 15 amp breaker is inside the headlight switch.
The headlight circuit is the longest and weakest. Chrysler used the minimum wire & terminal sizes for the job - 18 gage to the lights, 16 gage to the dimmer switch. Usually its not just one poor connection like a switch, but a the combination of resistances then topped off by one really bad one. That list 67Dart273 covers all of the junctions for the headlight circuit. However, the power comes from the main circuit - and any voltage drops along the way to the headlight switch will also result in the headlights trying to draw more current. (The headlights want power. When voltage drops, they try to get the power by pulling more current). So it is also important that the alternator's output circuit is in good condition, as well as the battery connections.

In my experience, it is worth checking each connection including at the headlight switch. While doing so look for evidence of oxidation on the copper at the terminals - an oxidized wire will carry less current, as well as evidnce of heating. Then look for chafing of insulation. For a non-concours car that is driven at night, a relay system is well worth it.

If you want to narrow down the search, remove a lamp and measure the voltage going in. Compare that to the system voltage. System will be battery positive if the engine is off, alternator output if the engine is on. If the voltage at the lamp is more than a few tenths lower than system, there's resistance somewhere(s). If not, then the problem is probably in the ground. An in-betweeen place to check for voltage drops is at the bulkhead connector.