If you do not have a train on track how do you get a Signal strength test. That test what the engine sees and responds to.
That is a pretty old set. Since no change with a tether, that rules out the receiver and transmitter on the units. You could try a different remote, or try your remote with a different TIU.
I would guess the TIU is going bad though. Whether it is repairable or not though is questionable. G