That’s pretty much the long & short of it, although if the regulator circuitry in an alternator goes TU it can short out and there’s only a fusible link (no fuse).
Ain’t carz fun?
The voltage regulator is a bunch of diodes. Diodes make great fuses when things go wrong.
Not quite sure if I understand what you’re doing. If you positive is hooked up and your negative isn’t, then getting 12v or -12v seems normal providing that the actual car is grounded.
Best answer? Bring it to Autozone or O’Reilly’s auto parts. One of them will test the battery for you.
If you’ve been in some extreme cold weather for a while, old batteries do tend to die because of the increased Cranking amps needed for cold starts.
If you think it’s an electrical fault, pull all the fuses except for the starter, voltage regulator and ignition. Then push them in one by one and watch the voltage across the battery.