Can we change the direction of a neurological signal?
"Neurological signal", or as I would put it, action potential, or activity propagation can be modeled as current in an electrical circuit. Trick is that such a circuit contains a bunch of highly regulated and non-linear and non-static elements. Imaging bunch of potentiometers (variable resistances) in your circuit. And all of them behave depending on something else in the system. So certainly currents will go somewhere, but level of control and complexity is phenomenal.

An example that should let you appreciate possibility of rerouting is simple Pavlovian conditioning. Neutral stimulus (bell) that has no evident connection to stomach, after conditioning elicits response there. Even though circuitry is very complicated and signal propagation is hard to investigate, this is an evidence that changing path of signals is very possible in some way. (Of course, conditioning require changes in higher-than-stomach systems, some intermediate levels).

On more practical note, we can readout neuronal activity in region A (of brain, muscle or else) and rely it via electrical stimulation somewhere in brain or muscle or gland. Both parts of this are available technology. As of drugs, some people report "seeing" sounds while intoxicated, this might be an example of such temporary effects.