Has it been dropped at any point? it sounds like there is an issue with the connection between the trackpad surface and the controller board within the battery compartment, but that doesn't typically just wear down. it sounds like it has suffered from a knock of some kind.
The only other possibility, which you have already ruled out with your tests, is if there is some interference to the bluetooth frequency. But as you've tried it on multiple machines, and have used other bluetooth devices in the same work zone, that near enough rules it out.
They are so fiddly to work on, so typically when a fault like this occurs, its not worth the time tracing or diagnosing unfortunately. so unless you can see some physical damage that can be repaired, you may have to write it off.
Sorry, i'm sure its not the answer you were hoping for.
The parts can be removed and inspected, but it requires dismantling the battery compartment, typically through the antenna cover on the underside first. it'll be adhered to the body, then you should see some philips screws to release the controller board through the end of the battery compartment.