Do they have a relay in the circuit? If not, consider adding one for each circuit (dim and bright), with the positive side fed directly from the battery with a large enough gauge wire. Locate them closer to the headlights, so there’s as little current drop as possible.
Then, the current circuit through the switches just controls the on/off and dim/bright switch functions, while the new heavier-gauge circuit provides the power for the lights themselves…
Early FF TDr on 69 VW pan
Slowly coming back from the ashes...