Hi Bill,
It is not only the gauge of the wire but, in original form, power passes to the headlight switch before flowing through the dip switch on its journey over a number of connectors to the headlights. By having power pass over larger gauge wire from the alternator/generator/battery through the 30Amp relays to the lights, power loss from multiple connections (switches and harness connectors) and under-sized wiring is eliminated and your original switches and harnesses handle only enough power to switch the relays and light your panel, parking and directionals.
Remember, your unfused circuit consisting of 45+ year old switches and harnesses designed for lighting technology of the 1950s. In that day it was common to have headlights with between 25W and 40W of draw. Today, headlights of between 55W and 100W each are not uncommonly installed on Healeys. Add the draw of a set of driving lights on this same unfused under gauged circuit and, along with your panel, parking and directionals, you have a formula for disaster.
Also, I agree with TimK as additional fusing is, in my opinion, critical. I have installed approximately 13 additional in-line fuses covering all critical circuits. I chose in-line as it was easier to select a specific circuit and hide the fuse. Due to my ageing memory, I was forced to create a directory of fuses and their locations.
Hope this helps,
Ray (64BJ8P1)