If I was to cut a hole in my electric guitar where a pickguard would be, would it cause problems with the sound of the guitar? I want to create a steampunk guitar with working clockwork on the right side of the guitar. Would the cut hole affect the sound overall?
Provided that you will not disconnect any wire (e.g. from or to potentiometers, jack or pickups) and the guitar is not a semi-hollow or hollow model, it would not cause any problems or significant change in sound.
(Assuming for a solid body Electric Guitar)
No it wont effect the sound.
As for your working clock. Guitar pickups consist of magnetic material, which produce a magnetic field, so depending on the material of your clock's inner components and placement near the pickups you may effect the clock function.
Electric motors are EM emitters, so clockworks that rely on an electric motor may introduce audible noise into your guitar signal. Presumably the motor will be fairly close to the wiring harnesses.
In addition, electric guitars--especially with high gain amplification--pick up mechanical tapping and knocking on the body of the guitar quite well, so any mechanical vibration a clockwork makes (even [or especially?] if not powered by an electric motor) may introduce audible signals.