What are some good ways to trace wires in an engine?

Something chewed the wires in my car’s engine recently. What are some ways to trace which wires goto which components?

Backstory: a few months ago, my car started acting funny. One of the blinkers was faster than the other. The ABS and Tire Pressure lights came on even though I don’t have those. My parking break light won’t go off anymore. And both my passenger bright headlight and AC don’t work. The car still runs well though, so I’ve been holding off until now so that I can do it myself if I’m capable. It’s a 2006 Corolla if that helps.