Without seeing a schematic of the lighted switches can't say for absolute sure. But, I will bet the problem is in the switch panel. Just take the wire off the switch and ground it. This way there is nothing to backfeed. If 12 volts from the light portion of the switch goes to the coil on the relay you meant to ground to activate you now have 12v on each side of the coil. No potential difference, I MEAN VOLTAGE.

Leon