The only wires that need
to be connected for the auto-dimming mirror to function are the accessory (key on) power and ground connections. The rest of the wires (if any) are necessary for the auto-headlamps feature (if your mirror has that feature).
In your initial message, you indicated that you checked the wiring and it was right; if that's the case, then the auto-dimming function in your mirror is broken, or you didn't check your wiring carefully enough.
Using your DMM, connect the black (ground) lead to the ground wire going to the mirror, and connect the red (+) lead to the accessory power (I think
it's orange/green) wire going to the mirror, and turn your ignition key to the "Run" position. Your DMM should read approximately 13.8 volts if that circuit is wired correctly. If it doesn't, then there's a wiring problem.