Good chance the pump is shot. Like above, check the motor ground VERY carefully. Fluid level OK? Does the motor stop, or does it always run, and just the movement stops?
To me it sounds like there is some sort of overload protection kicking in. A self-resetting breaker if you will. The load is too high so the breaker trips, you must wait a few minutes for the breaker to cool down and reset. Same sort of thing as the headlamp switch. I just don't know if such a system was used in the old verts.
If that's the case it could be caused by a faulty breaker/switch, the pump having to work too hard, or the motor wearing out.
No relay, but there usually is a breaker located on the starter selonoid battery terminal that is the feed for the pump motor. It will have a large wire (#10?) attached to it that will enter the firewall.
Normally letting it cool off will reset it, although it could be bad.
A voltmeter or a test light should be used to test the electrics. More than likely it is doing its job and the motor has issues.
There is a circuit breaker located by the starter relay. It should have a large red wire heading back to the pump. The pump stops because that breaker is tripping due to an overload. Mostly like your pump motor is burning up and drawing too much current.