Does the gauge of wire make any difference when wiring the inside of an electric guitar?
It's all fairly high impedance circuitry inside a guitar. Pickup to tone control to volume control to jack etc.. It's extremely unlikely thinner wire (or even the thinnest wire you could get hold of and be able to solder to) would have any effect. Given also that the amplifier/speaker is likely to tone shape things, it would be trivial to consider such things as skin effect increasing the resistance of a 0.2 ohm (dc) wire to maybe 2 ohms (20kHz).