IF you have a voltmeter and know how, you can use it to test the yellow wire to ground (green). You should have approx 12VDC if the circuit board is calling for 120V to the HWH. This DC voltage could be read at both the board and inside the plastic relay box.
When testing in the box, I caution you, there is 110VAC present at all times on the black wires and present on the white wires when the relay is closed.
Working around AC voltage can be dangerous and even deadly. Don't do it if you aren't confident with it.
However, since all of the connections are good, you could just do as 16ACE27 suggested and replace the board. It is the most likely problem at this point.
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