Trodzen...
I suspect you have too high a resistance somewhere. I would expect more than 12 V at the terminals, with no load. Take off the red and black leads, switch on the key and see if you could run a wee load there, say a 12V bulb or something. The classic symptom of corroded connections is that the multimeter will read close to 12 V, but the
lines will not draw a load as a corroded connection chokes off the current supply.
If it chokes off, check for corrosion in the supply wires.
I've ben there with that one a few times.