I have had my new gel battery run down twice since putting in a new cheapo Chinese R/R in my 2010 R3 Roadster.
Why did you replace the R/R?
... Each time after fully charging the battery in the bike I measured the voltage at the battery terminals when running at idle at about 12.6v with a fully re-charged battery. When the throttle was increased gently the voltage dropped to about 12.4....
Does this suggest my alternator stator is cactus and needs replacing?
That voltage is way low ........
You (presumably) had an initial problem and you changed out the R/R - you currently have a problem, which possibly (probably!) suggests the R/R was not the problem.
My experience with FH012 is that they are VERY reliable; and fact you have a problem currently also suggests that the R/R is/was not the problem.
That leaves the stator .........
Stator current - all three legs should be the same;
The way a Shunt Regulator works is that the stator is normally flat out at whatever rpm and whatever current is not sent to the Load (the bike) is shunted back through the R/R to the stator;
if you have one phase lower, it suggests that phase has a problem;
if a Regulator problem, it would typically be short and so current still 'max'; since it is 'low' it points to the stator.
There is a VERY simple test for a stator where you do not even need to power it on - unplug the R/R and measure resistance from any ONE of the three terminals (going back into stator) to engine ground; if you get a short, your stator is toast. You will get the same reading from each terminal to ground, because from pin to pin the resistance is very low (<1 ohm); so they will either all be short or none of them will be. So you can check all three but there is really no need - just pick one of the three and measure with respect to engine ground. It should be completely OPEN (infinite resistance)
I would still put in a small switch next to the dial as that constant draw would have a bigger effect on the much smaller 18Ah battery in the Rocket.
Voltmeter is going to have a fairly low power draw - if it has an LED display that would tend to draw more current than the voltmeter itself and that would depend on the specific device
However a small relay (compact reed relay - does not have to be an automotive type!) - is a good idea and makes switching on automatic.
You can also just connect it directly to an ignition-powered signal, but depending which one, you will likely have some drop from actual battery voltage. Consistency (or difference) is what you are looking for however, so even if it reads half volt less than battery then as long as you know that, it is fine. You can measure voltage at different points and decide which you can 'live' with.