Mice LOVE to chew wiring so there is a very good chance it has other damage points; I would pass on this one.
Two years ago I went out to run errands in my 2006 GMC 2500HD diesel pickup and I noticed the check engine light was on before I even put the key in the ignition. The truck started and operated normally but once started it would not shut off with the key and I had to pull the ECM relay to kill the engine. The only stored trouble code was a loss of communications between the engine controller and separate controller for the Allison automatic transmission. The next morning I went out to do more investigation but the truck was operating perfectly normally with no CEL and was like that for another month before the symptoms returned. Sorry PETA :)
I bought the service manuals for the pickup and made some measurements. Two hours of reading and an hour of troubleshooting narrowed the problem to voltage on the switched 12 volt bus even when the ignition was turned off. I found when I reconnected the batteries the voltage on this bus would slowly rise until it reached 10 volts and then the ECM would command the power relay on providing a full 12 volts even though the ignition was off. A few more measurements and I found the problem; a mouse had been using the top level of what GM calls the UBEC or underhood bussed electrical center as its urinal. The top level holds fuses and relays and underneath that is bare copper bus wiring running through guides and this layer provides the various circuit interconnections. The mouse urine caused corrosion in this second layer and when the humidity was high enough (thus the intermittent nature of the problem) the corrosive residue was sufficiently conductive to allow leakage between an always on 12 volt bus and the switched 12 volt bus. I found a replacement UBEC on ebay for $60 and it took about 15 minutes to change.
I now keep mouse traps in both garages. I live in the IL countryside and I believe what happened was a mouse decided my garage was a great home after the field he was living in was harvested. But once he went for the bonus cheese in the trap he suffered terminal structural damage.