IMHO. The relay kit is putting a band-aid on a problem.
Assuming the factory did good engineering, thousands of 60s convertibles without a switch issue. there must be a current draw somewhere. Maybe it is high resistance in connectors, loose connectors etc, maybe it's the pump motor, maybe the rebuilt switch was not rebuilt well, maybe it is a replacement wiring harness with wires that are not the correct gauge. (I use to source wiring from china and when measuring strand dia and counting the strands they all came in 1 gauge lower than requested, IE 18 gauge measured closer to 19)
THAT BEING SAID...
I think a relay kit would be a great idea, but after the root cause is sorted out.
Again just MHO
