Wiring Problem

Regardless of what a voltmeter says,known good battery, when car is running voltage needs to be minimum 1 volt above battery volts. So if your suspected faulty voltmeter reads battery at 11.5 with key off, then you want to see 12.5 with engine running. No less. Should hold that with loads on, fan,headlights and so on.

Perhaps a better piece of diagnostic equipment is in order.