the relay/solenoid is just a switch and coil.....the low voltage/amperage (12 volt coil) switches the high voltage/amperage contacts for the starter to engage.

jumping the terminals point to a problem after the solenoid. test the coils side with an ohm meter (unit disconnected)....if you have resistance, coil is most likely good. the fact that it pops after engaged, backs that up. test continuity across the battery terminals with and without the coils side engaged. if you have no resistance across the terminals with the coil powered, the solenoid is good.

if you have you have problems after it is in the circuit, the problem is after the solenoid.