The role of the voltage regulator in the SOHC4 is often misunderstood.
The "regulation" it provides is really only one that protects the battery from overcharge. IE. not allowing it to go over 14.5-15V, as at that voltage the battery is full and charging should be be discontinued or drastically reduced.
Recharging does a chemical conversion in the battery (the reverse of discharging). However, once all the chemicals have been converted, continued input of energy starts separating the chemicals rather than converting. The battery appears to be "boiling", but what is really happening is the hydrogen and oxygen are being liberated from the chemical solution via electrolysis. (Recall high school chemistry where applying DC electricity to electrodes placed in water separates Hydrogen and Oxygen from the respective electrodes? Hydrogen bubbles from one electrode and oxygen from the other.)
The SOHC4 voltage regulator has the primary function of NOT overcharging and damaging the battery. The bike system voltage is dominated by the battery charge state. If the battery is charged, it is the battery that dominates what the system voltage will be. I think of system voltage regulation as being the battery's job. The charging system is just maintaining the battery in a charged state when it can.
The SOHC4 Vreg uses the the black wire for two reasons, to sense battery voltage, and as a power source that is passed to the field coil when the voltage it measures shows the battery isn't fully charged. So, it should be noted that if the black wire isn't reporting truly, the vreg can't be blamed for malfunction. Lie to electronic devices and they become confused and make wrong decisions (HAL syndrome).
Further, low voltage received on the black wire is passed in full to the field coil, and the field coil strength (and RPM) determines how much power the alternator can make. Less power in = less power out, in ratio.
The SOHC4 "regulator" has only three distinct operating states it communicates to the field coil; Max power, medium power, and OFF.
Max power is indicated when the battery is discharged below full or discharging. However, there is no set time it remains in any of these states, and in fact, it can switch between the three in time slices that are determined by battery state, alternator RPM, and system bike electrical load.
Consider a battery full @14.5 V. The vReg tells the alternator to put out half power. However, half power isn't enough to run the whole bike, and the battery supplies the difference which lowers the battery voltage (slight discharge). The Vreg sees that and tells the alternator to switch back to full power, charging the battery back up. The Vreg sees that and switches the Vreg back to medium. See the cycle here? The regulator is switching things on and off at a frequency, which we do not and don't normally need to know.
Measuring issues:
Another bit of confusion can be introduced by how a digital multimeter collects and displays information for the technician to interpret. As you may have noticed the display doesn't remain at one number, it changes. Digital devices have a screen update time. There are many meter designs. But, to give you an idea, the device may sample the voltage source 10 times a second, it may update the display at 1/3 second intervals, and it may or may not do a statistical math operation on the samples collected.
The meter's update and change frequencies may or may not coincide with the Vreg state change frequencies. For example, if the battery is changing between 13 and 14 V because the vreg is switching the alternator on and off, the meter reading could possibly synchronize with the 13-14V transition and only display 13.5 V. A digital device is possible to synchronize with random events, as synchronized events are a subset within random. Further, the numerical alignment and un-alignment of collected samples and device states is infinite. In other words, a meter can synchronize with events contained in a random field of samples, and report something that is really not truly characteristic of the occurring events.
In my opinion, while your Vreg may be bad, you have not proven it so, as you haven't determined how it is or is not controlling the alternator when the battery needs it (or not).
The white wire to the alternator receives output from the Vreg in three states; Full passing of what is on the black wire, 1/2 of what is present on the black wire and 0V.
To declare the Vreg as bad, you have to check at least two of the states; Full and 1/2 power. For full power the battery needs to be below, say, 12.5 V. And when the battery is between 13.5 and 14.5V the white wire should have maybe 6V -ish. However, if the contacts are chattering or "hunting" between the two states, your meter and battery may average that sampled voltage anywhere in between.
Be certain that the "sudden drop" you noticed isn't just the result of the charging system finally restoring full charge to the battery, and the vreg responding with "that's enough full power".
However, if you can measure the battery at 12.5V and the Vreg isn't passing all the voltage it gets on the black wire over to the white wire, the Vreg is not doing the job correctly.
Something you might do is try changing the bike system load during testing and collecting voltage data. Pull the headlight fuse, which will remove 50-40 Watts from the system load trying to drain the battery. The battery should still never exceed 14.6V. But, the Vreg switching frequencies will all change with the load change.
Have you checked that the Black wire closely represents what the battery voltage really is, both with headlight on and headlight off?
Hope this helps,
