@Larry Fine , just remember the connector as shown in your adapter photo 1 is always from source power. The covered pin on an SAE connector should also represent source power. That is so that any pin with power on it that may be unplugged is not exposed resulting in potential to short out against something like frame or you.
@ST Gui , I use a remote variable controller that I mount on the body of the bike in a convenient location. I don't have a jack mounted IN any of the panels. This allows me to easily remove all but the fuse holder and a short pigtail from that for the entire heated gear system during warm months of the year. I will also remove the fuse during that time. It also allows me to move the entire system from one bike to another when I change rides. So I still have the same system, controller and cables and gloves, as I had when I first bought it when I owned my 2005 Burgman 650. I simply moved it all to my ST1100, then to my CTX1300, and now it's on my 2013 Burgman 650. Here are a few photos of where I had the controller mounted on a few of those rides. There is a 18 inch cable from the controller to the coax connector for me to plug into. This is what disconnects when I leave my ride, either intentionally or not.

This is on my ST1100. Under the false bottom in the glove box is where I put my Aux fuse box and still had usable space on top of that. The cord/connector with the red band is the source for the heat controller which I had mounted on that panel just below the photo.

If you zoom in on this photo you will see the leather holder for the variable controller just below the glove box. This is the last install where I used that case since it started to fall apart when I tried to install on my CTX1300.


Here is how it was installed using
Dual Lock (like Velcro only much better) on the gas cap door. One photo with the seat off and one with seat on. That same cable end with the red band can be seen in one of the photos.


And here is how it is mounted on my 2013 Burgman 650 using Dual Lock. It was mounted on my 2005 Burgman 650 very similar to this. The battery and my Aux fuse block are under the nose of the seat on this scoot. When I open the seat to get to the 50 Liter storage box under there I also have easy access to both battery and fuses.
There is a red LED just next to the knob on the controller that flashes per how hot I have it set. Slower flashing is low heat, faster flashing more heat, solid ON is max heat. I only use max heat when temps approach zeroF. I have always mounted this controller so I can see the LED easily, even in my peripheral vision sometimes, and also to make easy to adjust on the fly.
As you can tell if I leave my ride for any reason the source cord coming out of the controller orients itself so that the connector at the end easily unplugs with very little force.
Oh, and BTW, my knees and hips LOVE the step through. The engine on this scoot is frame mounted just under that step through panel and extends back under the battery/seat area.