If you want to rule out most of the wiring as an issue, simply run a jumper from the battery + to feed side (switched 12V) of the ballast resistor.

This will eliminate everything from the battery to the the ballast. Heck, you could jumper out the ballast to eliminate that too as a temporary test.

They say there are no such thing as a stupid question.
They say there is always the exception that proves the rule.
Don't be the exception.