I can't seem to find information on this, but what are the properties of the signal passing through the guitar cable? What I mean is, if I were going to make a pedal of some sort, what sort of input to the pedal from the guitar and output from the pedal to the amp would be used?
The signal between an electric guitar and a guitar amp is called a signal voltage. The voltage in the line oscillates in a manner analogous to the strings' vibrations, summed. The level of the voltage is dependent on lots of things including string material, how much energy is in the strings, and the electronics of the guitar. There is no specific standard, but the level is generally called "instrument level," which is below line level and above microphone level.
It can range from a few millivolts for passive [magnetic] or piezo pickups to several volts on instruments with active pickups and built-in preamps.