WARNING: Tube/Valve amplifiers use potentially LETHAL HIGH VOLTAGES.
Building, troubleshooting and testing of these amplifiers should only be
performed by someone who is thoroughly familiar with
the safety precautions around high voltages.
For line level signals with no real current I tend to use 24awg (larger than required for the amount of current involved, but thinner wires tend to be more difficult to use and aren't as strong).
Have a look at this link which describes the awg required for different currents:
I think signal doesn't really have much current. I guess what I really want/hope to know is if there is any benefit of using a thinner or thicker wire for signal within the chassis.