How long does it take for the computer system to.

The relearn is a matter of meeting certain conditions while driving, not a matter of time. The generator has nothing to do with any relearn. If it isn't working, first verify the "Battery" light on the dash works. That's the circuit that tells the voltage regulator to turn on. If that's working, look for a blown 15 amp fuse. If you don't find a blown fuse, measure the voltages on the wires on the generator with the ignition switch off, then with it on. Holler back with the wire colors and those voltages.