I've got a '66, but I presume the 4-way
flasher system is the same. Power comes from the fuse panel, to the em
flasher, (up under the right side of the dash) and then to the switch on the overhead console and lamp. The other side of the lamp then goes to the 3-pole relay in the trunk for the rear lamps, and to the 4 pole relay for the front park lights, fender repeaters, overhead lamp and then to ground. If your light is staying on, and the lights are not flashing, I think you must have a short to ground somewhere in the trunk-mounted relays.
As you found, pulling out the
flasher makes no difference as the power wires are paralleled on the pin.
On the fuse panel, the feed wire for the
flasher circuit is #383, a red wire with a white tracer. You can pull that fuse to turn the light off until you find the problem. It will not affect any other circuits.
Cheers