What year is your car? The wiring changed several times between 1979 and 1993.
Your problem is coincidental, there is no direct connection between the voltmeter and the alternator.
The voltmeter gets power from the switched side of the fuse panel
The following are diagrams courtesy of Tmoss & Stang&2birds
Fuel, alternator, A/C and ignition wiring
Ignition switch wiring
See the following website for some help from Tmoss (diagram designer) & Stang&2Birds (website host) for help on 88-95 wiring; http://www.veryuseful.com/mustang/tech/engine/ Everyone should bookmark this site.