C5,
The wire you call out on your regulator is just plain old solid 18- 22AWG hookup wire. As was mentioned ealrier, there are no "protective" devices or fuseable links inside the regulator (but fusing the SG really isn't such a bad idea.)
Here is another view of the same regulator.
The wire connecting the relay to the terminal is probably to support field current (I'll have to check and get back to you). In either case, field current or relay voltage sense function, #18 - #22 AWG wire should be fine.
The relay to the left is the current sense relay. Note the much larger physical size of the wiring wrapped on this relay. The current limit relay activates from the magnetic force developed by a few wraps of larger gauge wire carrying up to 15 amps of current .
The voltage control relay consists of hundreds of wraps of smaller gauge wire whose function is to respond to the voltage present across its contacts.
Either relay, when activated, can remove the ground from the field of the generator - shutting down power production. In order to keep the generator from slamming full on to full off, a power resistor or resistor(s) in some setups (shown below)
allow a minimal amount of field current to flow even when the regulator cuts off the ground to the generator. With the power resistors functioning properly, the generator is either full on or "somewhat" on - never fully off.
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