Ok, so I went and did the experiment. With the engine running with the headlights on high beam, the alternator voltage is 13.7, and the voltage on the headlight plug is 11.6.That's more significant than I was expecting. 
I might go down the headlight relay alley first. At any rate, it should protect the stupid headlight switch which I've already had to replace. 
Also, the headlights themselves are somewhat full of red dust. I reckon a bit of a washout might help. 
 
My biggest problem with the whole system... is my light bar is driven by a relay and is plenty bright. However when you have an oncoming car and you have to dip the beam it's like you are plunging down a mineshaft with a miners lamp. So I'm not chasing high beam.. more low beam.
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