Could anyone tell me how much pressure I should use to test my heater core?

The same as the cooling system. 14 PSI.

I would test it with a bit more pressure to compensate for the temp difference. More towards the 18 - 20 psi @ room temperature.

Fill it with water and use air to pressure the core. You want as little air as possible. Let it stabilize for 15 - 20 minutes check the pressure and then again after another 15 minutes. The reason for this is because its full of water and very little air. The water temperature has to be stable and the same as the surrounding temperature. After that the smallest leak will show up quickly.

An alternative is to fill it with air and submerse it in water and check for bubbles.

Chas

Thanks Guys, Now I can finish my heater system. I disasembled the whole system, repainted in and out, replaced the flap seals,foam seals,and installed a Honda blower. If the core checks out I just need a water valve.