the alt is grounded thru its case. the regulator should be grounded also. i think the brown wire should have power with the ignition on. i dont think the regulator will work without an ignition signal. the orange wire should have power all the time, the blue wire should have power when running.
if the alt tests good, and you have power to the brown wire with the key on, i would replace the regulator with a new solid state to eliminate it as a problem. check it for ground with an ohmeter, as it can corrode, or be separated by paint. the frame of the regulator needs to be grounded where it mounts.