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The problem is your control board. Unless you have a broken wire between the drain pump and the control board, you have a faulty relay on the board and the control board would need to be replaced. It's really common with this model washer where the drain pump relay on the board fails and stops sending power to the pump. Now testing is tricky because if you unplug the pump, you'll likely read 120 volts during draining, but in reality there is a voltage drop when you plug the drain pump in. That will cause the voltage to drop down which is why the pump doesn't run and the voltage checks good when you unplug the pump. Either way, replace the control board to resolve the issue.
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Either the board came faulty or you have a broken wire between the board and the drain pump. There are absolutely no other options. So if you have confidence in your board, you'd need a new wire harness. You can test continuity through the wires to see if you have less than 1 ohm between between the drain pump and the board and if not then you need a new wiring harness---otherwise your board came faulty.
It would as long as the wire harness was still plugged into the drain pump and into the board and you weren't testing to ground, you were testing between the power and neutral wire which goes to the drain pump.
OK then I'm not sure of why you're confused. There are 2 options as I mentioned before. Those are the ONLY 2 options. That means if you believe you tested correctly and the control board is good, then you have a bad wiring harness and you need a new wiring harness.
That I can't see without following them if I were there in person so that is what you would need to do.
No problem and good luck.