I thought the relay got 12 VDC from the key when you put it in the run position. That started the timer in the relay and when you cranked the key to the start position it sent voltage to the starter.
In my VW truck, I had the contacts get all fried in the back of the key from the heavy load of the system so I put a relay in that gets a feed off the ignition. When I turn the key it turns on a Ford Truck relay that sends power to the glow plugs. It also sends power to another relay that will send power to the started when I hit a momentary switch on the dash.
So I turn the key, count to about 20 if it is a cold morning, and then push the starter button. Varrooom off she goes.