Light indicates 12 volt system is "Live) sounds like you have two wires reversed. YOu can switch them at the switch.
THere are 4 wires on teh switch. Two are the control wires to the solenoid (you can reverse them at the solenoid if you like) and the other two are power and ground.. You need to reverse two wires. does not matter which pair.
HOWEVER.. I like to have the control wires at GROUND potential when the switch is not pressed. So use a volt meter or test light and if they are Cold/COld (No light or voltage) reverse 'em at the solenoid or the switch. If they are HOT HOT (Light or battery voltage Reverse power and ground at switch.
Or just turn the switch over.