If possible, and if you have not, you need to pull the switch out so you can access it. Maybe there is a really poor connection somewhere, just good enough to show power, but goes dead with a load
What all in the car works and what does not ? I assume this is a 67 Barracuda? You did not say or I missed it.
DOES THE hi beam indicator work? That branches off (red) at the interior side of the bulkhead connector
The dimmer is red, hi beams, bk, low, and light green, HL power coming from the light switch. B1 at the light switch is NOT fused (other than the main fuse link) and comes direct from the welded splice in the ammeter circuit
B2 feeds the park / tail circuit and also the inst lamps. That fuse also powers the 4 way flashers. That fuse on the diagram shows as 2nd from one end, next to the small INST fuse.