The solenoids look the same 6v and 12v. There is a short throw and longer throw. You can check the length of the throw with a jumper wire and battery. When I converted mine from 6v to 12v I was going to use a 12v from a mid 60’’s GM but the throw was wrong. I used a solenoid from a 60’s ford that matched up and works fine. I don’t have a relay in it. I use a single wire with a toggle switch.

Thanks Ed. I have heard of people using a switch. I might go that route. It's getting hard to find some of this stuff - cars from the 60's are getting scarcer and they didn't all have overdrive!