I don't think your heart needs to sink, as you've provided a focus, narrowed things down nicely.

If the results of moving the "bad" sensor to the other side is that it suddenly becomes "good," you won't have too many variables to address. Making a guess on your connectors, I would suggest to examine that all leads of the specific connection to ensure the tiny metal prongs inside the plastic housing are pushed fully into the housing. The metal prongs are slightly spring loaded and the back side has a finger that sticks up in the opposite direction. When the prong is pushed into the housing, the finger pops up into a recess, preventing back travel. If the finger doesn't get fully into the recess, the prong can be pushed backwards when the connection is made.

If that doesn't solve the problem, you could have a cold solder joint. Those can be visibly obvious but can also be invisibly "un-obvious" and require a touch with a hot soldering iron to resolve.

It's best if you can identify the specific wire and the contact points at each end. It's apparent that the module assembly is in acceptable shape if you can move it completely from one side to the other. That leaves the connector into which it plugs (or is it a sub-board) on the way to the main board?

More details about the cable routing and connectors involved would be helpful. Photos might be helpful but not necessarily, as it could be challenging to get suitable detail amidst a bundle of wires. Photos of the connectors involved in the circuit would be good.