My a/c compressor only works when I connect the negative from the relay straight to the battery negative. What could be the issue that the compressor is not engaging. How do you jump the termostat under the glove box? where does the power come from for the termostat? I try testing it with a volt meter and I get nothing.

 

I car don't have an AC so I can't duplicate your problem. But, on the old civic, your symptom seem to point to a bad compressor switch which locate on the compressor itself.