There is test in archives.
But here goes.
There are two wire going to pump to supply voltage. One is a nutral or ground and one is the positive lead. I beleive that the black wire is ground. This can be checked with continuty tester.
Then take a wire with clips on it and connect it to positive and connect other end to Pos. of battery. You will eather hear it running or feel it running. It it does run pumps bad.
In archives there are articles about cutting the positive wire and inserting a 1 amp slow blow glass fuse and holder to protect the Climate control unit from burning out. Climate Control
unit is $300 to replace. The fuse and holder may be $5.00. To me that is cheap insurance.
The above test is done on the car with all plumbing attached.
Good luck.