OK... so the DOHC R/R differs from the SOHC R/R in that instead of increasing or decreasing the voltage output of the R/R in order to modulate the field coil, the DOHC R/R varies the resistance on the return circuit. Ohms Law means that an increase in resistance causes a drop in current, so as the resistance increases, the field coil gets weaker. The increase in resistance is something we can measure with a multimeter.
Before we get to that point, there are a couple of other, easier, tests we can do.
First up, unplug the black wire that leads from the R/R to the alternator and then turn on the bike and flip your kill switch to off.. Using your multimeter, check DC voltage between this wire and the negative terminal of the battery. You should have about 12.5V if everything is working correctly. Plus or minus a few tenths is nothing to worry about. If you're getting no voltage or anything under 10V, stop and we'll take a look at this problem.
That first test is to ensure that voltage is actually getting to the alternator. No power to the field coil means no power out of the alternator.
Next, we'll repeat the test, but plug the black wire back into the alternator and unplug the white wire. Measure voltage between the white wire coming from the alternator and the negative terminal of the battery. Voltage should be pretty close to, but possibly a bit lower than, your first measurement.
This checks to see if we have power flowing through the field coil.
If both of those tests check out, we'll want to remove the R/R from the bike and perform the next text on the bench. This isn't a super-simple test, but it gets the job done. I use an adjustable power supply for this test, but if you don't have one you can still get something together. If you don't mind spend the $$$, they're not very expensive and they're pretty useful for all sorts of things (including for use as a battery charger). Details here: http://www.ebay.com/itm/251705177148
Anyway... Assuming you're not using a power supply, you'll need a spare 12V battery (any 12V healthy battery will work). And a few spare household batteries (AA, C, D, etc). You may also need an extra set of hands. Alternatively, you can use a trickle charger that puts out more than 14V.
Hook up the 12V battery, along with two of the household batteries (it's OK to mix and match types) in a series circuit. That is, positive terminal on one battery to negative terminal on the next battery, and so on. Form a line until you have three batteries all in a line and connected. Because we're wiring the batteries in series, this will increase the voltage when measured between the positive terminal of the last battery in the line and the negative terminal of the first battery in the line. DO NOT connect the first battery to the last battery. This will likely cause things to get very hot very quickly and possibly start a fire.
Now that you have your batteries set up, use your multimeter to measure the voltage between the positive and negative terminals of your battery line. You should have pretty close to 15V, hopefully a bit over. Next, connect the red and the black wire (the two in the same connector) to the positive end of your battery setup and then connect the green wire to the negative end of the battery setup. Switch your multimeter over to read resistance and measure the value between the other black wire and your white wire. You should get a value over 100 Ohms (the value will vary based upon a number of factors, so you're really just looking for a reading that's fairly high).
Assuming that looks good, remove the extra household batteries for your setup and repeat the test using only the 12V battery. The Ohm reading between the white and the black wire should now be fairly low; close to zero.
How's that looking on your side of things?