Did the light used to go and off sensibly? Any recent work or changes? Voltage = 12.5V at 3,000rpm That's definitely too low. Are 90% of all alternator faults the voltage regulator?
What else should I check? Could still be a wiring fault. How many wires of what colour and thickness are connected to the alternator on how many terminals? Check belt. Check all connections including at the battery and the relevant earths: inspect, wiggle, disconnect, clean, reconnect. Then measure those voltages again, and if they're still the same, measure at the alternator terminal. Jonathan