Well, after trying almost every combination of sequences imaginable of what to pair and when, here are the final results:

The J&M

Can pair with the Rogue, with the Garmin 765T, and with the Zumo (individually) with no issues
The Rogue and the 765T will pair in parallel with the J&M but is a bit flakey on occasion
Can have either the Rogue or the Zumo paired with the J&M but not both in parallel

The Rogue

It will pair with the J&M
It will not pair with the 765T (consistent with Garmin site info)
It will not pair with the Zumo (consistent with Garmin site info)

The 765T

It will pair with the J&M
It will not pair with the Rogue
It will not pair with the iPhone

The Zumo

It will pair with the J&M
It will not pair with the Rogue
It will pair with the iPhone

Conclusion

There is a difference in the Bluetooth arrangement between the Garmin 765T (now discontinued) and the Zumo 660. While both are compatible with the J&M, this difference:

Allows the Rogue and the 765T to parallel up with the J&M
Prevents the Rogue and the Zumo from paralleling up with the J&M

Choices are to:

Ditch the Zumo (not preferred) and use the Rogue/765T/J&M on both bikes (R11RTP & R12GSA)
Ditch the J&M (not preferred) and go hard wired
Get a phone compatible with the Zumo such that the Phone goes to the Zumo and the Zumo goes to the J&M. (It would be too much to hope that some alignment would allow the Phone, the 765T and the J&M to work as well. Turns out it did work.)

Action

I used this situation as an excuse to get a new phone, one compatible with the Zumo, an iPhone. (I am an Apple/Mac guy anyway/all the way).

Result

The iPhone is compatible with the Zumo. So, I pair the iPhone with the Zumo and the Zumo to the J&M and it works fine. Specifically, the J&M is seen as a headset by the Zumo.
The iPhone is compatible with the 765T but the J&M is not seen as a headset. This means that while the music/directions will play from the 765T to the J&M, when the phone is used while paired to the 765T (same arrangement as with the Zumo) the phone output comes from the 765T speaker and the voice uses the 765T mic. However, this will give me hands free when driving the Jeep or the 65 Pontiac (Catalina, 421 HO Tri-Power, 8-Lugs, etc) but is still no good on the older bike.
Now, I could get another Zumo power cable and install it on the RTP so I can use the Zumo on either bike. That would be another $60. But, as luck would have it, the J&M will allow the 765T and iPhone to be in parallel, just as it did with the Rogue.

Summation

The Rogue would never pair with a Garmin properly.
The Rogue would pair properly with the J&M.
The iPhone will pair properly with the Zumo and is seen as a headset
The iPhone will not pair properly with the 765T, is not seen as a headset.
The Bluetooth protocols on the 765T and the Zumo are different.
The J&M will allow a parallel alignment with the 765T Bluetooth protocol and both the Rogue and the iPhone.
The J&M will not allow a parallel alignment with the Zumo Bluetooth protocol and either the Rogue or the iPhone.

So, until I get another Zumo power cable/cradle assembly for the RT (at which time I will just use the Zumo for both the RT and the GSA ÔÇô much preferred arrangement):
When riding the RT, will use the 765T and iPhone in parallel, both paired with the J&M. When riding the GSA, will use the iPhone paired to the Zumo and the Zumo paired to the J&M. Kinda the way it is supposed to be.

In closing, it appears that the Bluetooth Standard is not very standard at all. It is currently a matter of trial and error to figure out just what will work and will not work with various pieces from different manufacturers. The fact that the two Garmins, both with the latest and greatest upgrades yet operated differently, are a testament to this as well as not being able to count on the same manufacturer being consistent. I was happy with my J&M/Rogue/765T system. The Zumo through things all out of kilter. The iPhone brought things back in line. The J&M product was not the source of my issues. Garmin is/was. I am very happy with the performance and sound quality of the J&M rig and that is why I continued to pursue a remedy that included the J&M product.

As I have said before, Bluetooth is currently a hit or miss proposition. Before purchasing, look for input from people who ACTUALLY have the configuration you are thinking about. But, once you find one that works, go for it. Wireless is B-E-A-utiful.