from the symptoms I would say it's weak bimetal breakers on the switch, but if you're satisfied the replacement is good, then it has to be something in the wiring that's causing excess current draw .... make sure all your grounds are good, the ones from the headlights on the core support particularly .... a relay shouldn't be needed if you have the correct wattage original type bulbs [50W]
a correct original style harness runs 200 at
American Classic - and note at the left of the forum page, could be a good discount right now

Bill