Perhaps the contacts on the wiring harness connector and/or pump are dirty or corroded and preventing power from reaching the pump motor. I'd examine and clean the connectors, plug the motor back into the harness, and see if it works.

It again doesn't run when back in the machine? Is the impeller loose from the shaft, perhaps jamming when under a load attempting to push water?

Service info for WP's Duet Sport model, which reasonably is a sibling to an HE2, says 12.3 ohms on the pump. How long did you run it on the bench test? Run it long enough to confirm it's not going to high resistance under a load and cutting out on overheat protection.

I cleaned all contacts with electronic contact cleaner. However, the impeller does rock back and forth as if the shaft were loose. when I tested it in the washer, I just plugged the connecter into the motor and set the motor loose on the bottom of the washer. I saw this procedure on one of the videos on the internet. However, it should be running the same as when I plugged it in on the workbench. I don't have the filter housing attached to it. Just ran the motor on the workbench attached to an 120 AC receptacle for 8 minutes. Ran fine.

Perhaps I'm not underanding what you tested but is it possible that the loose impeller jams when the pump motor is attached? According to this webpage, the pump replacement part number is WPW10730972. You can pick up one of those on ebay for around $30 or even less.

I tested the pump with the filter housing off, on the workbench and connected to wiring harness. There was nothing touching the impeller. If the motor runs on the workbench, it should also run when connected to washing machine .supplying 120 V.