Charging Circuit info from Ionbeam (fjrforum.com)

Reader's Digest Condensed version:  Pull the DC output connector off the R/R.  With the engine at idle measure a minimum of 13.8 volts to a maximum of 15.8 volts.  If your FJR passes this charging system test, replace your 9 year old battery. 

If the voltage is still low at the new battery terminals you have voltage drops throughout your main electrical system harness.  There are several connections between the R/R and the battery and even more between the battery and the main ignition switched electrical system.  Every connection contributes a small voltage drop, including drops across the fuses.  These are the demons that dcarver has been trying to exorcise.

R/R (Regulator/rectifier) - does this unit typically produce a "hard" fail. i.e., Does it go instantly from working properly to complete failure? Is there a short (or long) interim period where it may not produce enough amps although still work, after a fashion? Will it produce the amps but perhaps not properly rectify the output from the stator? How many people have had to replace a R/R on an FJR?

 
The R/R will typically produce a hard failure and will most likely do it instantly; it most likely won't be a complete failure but there will be a substantial voltage issue.  A modern R/R is highly unlikely to fail unless the owner has done something to antagonize it.  The rectifier section is very unlikely to fail, if it does fail, the R/R will have very low DC voltage output.  If the DC regulator section fails, it is more likely to have a HIGH voltage output than a low voltage output.  In old school wet cell batteries with acid/water filler caps, the first hint that the DC regulator has gone bad is low water in the battery as the over voltage boils out the water from overcharging.

There have been very few R/R issues reported here.  What is harder to get information on is how many R/Rs were replaced where it was indeed the root cause of charging and electrical system issues.
 

Stator - I guess the same main questions... Assuming that the magnets remain intact and in their proper places, is a hard failure (i.e. wire short or open) most likely? Do you expect to see gradual "weakening" in terms of the stator being able to produce enough amps to keep the bike (and battery) happy? I assume this could be caused by magnets weakening due to heat exposure? Other causes?

The magnetic rotor is a uniform looking, cast piece, your assumption that the rotor is intact is good, the FJR's permanent magnet rotor won't weaken.  The stator is much more likely to fail shorted than open.  There won't be a gradual weakening, it will be good then bad.  There could be a very quick period where the stator is intermittent but it will quickly become a hard failure.  The vast majority of stator failures is caused by the enameling on the winding wires burning and cracking.  When this happens the windings short together or the windings short to ground.
 

Battery - I pretty much understand the (multitude of) failure modes possible...

Done.

Wiring - I think this is where I am going with this although it will depend on what I hear back from people. I read dcarver's (long) thread on the issues...I don't dispute the results but I am wondering if anyone has any insight as to why this happened; especially after many years of "normal" operation? Has anyone identified the specific connections where high(er) resistance has caused a voltage drop on the order of 0.5 V to 1.0 V? Are there any other wiring-related problems people have discovered which degraded charging performance? (Battery connections are an obvious (common) problem and I have double checked this)

Every place there is a fuse, harness connection or stud connection there will be a small voltage drop.  In the Gen II grounding system there are crimps within the harness run which may also develop voltage drops.  Over time dirt and oxidation happen at every connection, once it starts it will slowly get worse.  Fuses have a normal small voltage drop across the component.  On my Gen I the R/R to battery voltage drop was primarily at the stud on the starter relay where the R/R DC output wires are joined together with the heavy battery cables.

Anyway, my situation is that I am seeing less voltage at the battery than I like (13.3 at idle and 13.7 or so at 2500 rpm). I have had a couple of instances where the battery voltage had dropped to a point where the bike did not run properly and a couple of times I needed to boost it to start. Although battery condition is questionable (163,000 miles and over 9 years), it will charge properly with an external charger and will operate the bike normally with respect to starting etc. I am thinking it is at least partially charging while operating but perhaps not enough to sustain it...

Testing the stator:  The average DMM can't do a stator winding resistance check.  Due to differences in the Gen I & Gen II charging systems the actual stator voltages may be different than the stated voltages in the tests below.  What is key is that the voltages are all three equal to within 2-3 volts.

Pull the 3 wire stator connector off.  With the engine OFF, set the DMM to the highest resistance scale typically 10 meg or 20 meg. 

measure each pin in the connector to ground, the readings should be close to infinite resistance (no reading at all on the meter)

this verifies that none of the windings are shorted to ground

Set the DMM to AC volts, the range should be set for up to 100 VAC

Start the engine, let it idle then carefully --

measure all three pins with the red and black DMM probes going from any pin to any pin

at idle there will be roughly 20 VAC, don't sweat the actual voltage, the key is that all the voltages are equal to within 2 - 3 volts

if the voltage is wrong it will be wrong by a lot, beyond any doubt that it is different

Bring the engine RPMs up to ~5k

measure roughly 60 - 80 VAC any pin to any pin, don't sweat the actual voltage, the key is that all the voltages are equal to within 2 - 3 volts

if the voltage is wrong it will be wrong by a lot, beyond any doubt that it is different

the voltage tests verify that none of the windings are shorted together and none of the windings are open

If the stator meets these conditions it is good, no question about it

Testing the voltage regulator:  (put the stator connector back on), pull off the the connector with the two DC voltage wires

Set the DMM for 20 VDC

Start the engine, let it idle

measure 13.8 to 15.8 VDC on the R/R output pins, if it passes this test the regulator is good, no question about it

Passing the stator tests and the R/R test verifies that the charging and voltage regulation system is good.