It's the light switch. The switches that are sold do not stand up to the quality of the originals. Do the relay addition and no more problems.
With the relay the load for the lights is carried through the relay not the switch. The only thing the switch does is turn on the relay, which is powered and feeds the lights directly from the battery, thus no big draw on the light switch.
If you look on the old switch, and turn the knob you will see a coiled spring that is the part of the switch that dimms the dash lights. On the left side of the switch is a Bi-metalic arm that heats up and if the amp draw is to much opens the circuit and the lights go off, it cools down and the lights come back on.
When you install the relays the load is through the relays not the switch.
