What wire size should I use to repair a circuit containing some #12 and some of unknown size?
The wire gauge you need can be determined by checking the breaker for that circuit - if it's a 15 A breaker, you can use #14 gauge wire; if it's a 20 A breaker, you need #12. In general, lighting circuits are on 15 A breakers and wired with #14 wire, and receptacles are on 20 A breakers and wired with #12 wire. This convention is relatively modern, though, so your 1975 wiring may not follow it.

There is never a problem using bigger wire than needed, so even if the existing wiring was #14, you can replace it with #12 - just don't replace the breaker! A 20 A breaker needs #12 wire throughout the entire circuit.

You can also get a tool to measure the size of the wire. Something like this:



Or this multi-purpose wiring tool: