relay powered voltage regulator ?

You can use the resisted type as it's not a huge deal.
Here is a Napa part that will work just fine.
Electrical Relay - Universal - H/D Truck

There is also Dorman Part Number: 88069 at Autozone.

If you end up with a 5 terminal relay just ignore terminal 87A.
Relays with the 87A terminal can be used for normally open or normally closed switching both, so ignoring terminal 87A makes it a normally open circuit until the key is turned.