I vote with the group that says the electric pump ran when the engine ran. Before I removed the flat top carbs and the electric fuel pump, I could hear the pump running whenever I was stopped with the engine idling.

I'm in that group too Pat.  I guess quite obviously since I've been running with the electric pump only since 1979.  Those relays do the exact opposite of what was described, they make sure the elec pump is not running in event the engine stops, like in an accident.  Turning on start key enables the pump again.

Has anyone seen a Z with the "competition hood vent".  Actually, that became standard in the zx.