enblethen wrote:
There should be no resistance reading between either of the element wires to ground.
That is normal problem element goes to ground. Part of the load goes through to the ground which trips the GFCI receptacle.
More precisely, there should be infinite resistance (no connection) between the element wires and ground. This, an open circuit, may often be displayed as a non-reading on a digital multimeter, or as an overload or something similar.
Just don't confuse it with "no resistance", which is zero ohms or a short circuit.