I agree with Chas. Sounds like a relay. Some boards have an extra relay on them that you can swap over to, but I'm not familiar with your board. I believe it is normal for some tubs, for the heater to deactivate when the jet(s) are running so as not to draw too much amperage. The fact that the heater is deactivating initially may be telling us that the board is at least sending the initial voltage to the pump (as you tested), but the relay isn't staying closed. You say the relay reads 119v with no load when you push the switch, put as soon as you load it with the motor, the relay opens again. Yet, the motor runs fine when fed with a different 120v source. I know relays can get sticky, but is it normal for them to act funny only when a load is applied?