In my experience, a 12 volt relay will close on 6 volts.
I have an old Willys Jeep, 6 volt system. It has 6 volt relay to connect the starter to the battery, and the starter relay is wired so that GROUNDING the small terminal causes the starter relay to engage.
I wanted the Jeep to start by turning the key. The ignition switch supplies power to the start terminal on the ignition switch. This does not activate the starter relay.
I took a 12 cube "Bosch" relay, and apply power from the ignition switch to pin 86 of the relay. Pin 85 is grounded. Pin 87 goes to the Jeep starter relay, and Pin 30 is grounded.
Turning the key to "start" energizes the coil of the cube relay. The relay contacts then ground the Jeep starter relay, and the engine cranks.