I'm not aware that OE (pure stock) bikes have a SAE plug anywhere on them. If you pull the seat, unsnap the big rubber band, roll the radio forward on it's wires, and pop the battery cover, you will probably see that the SAE plug you have under the side cover runs up to the battery terminals.
The Aux plug is round and has a rubber cover over the terminal.
Obviously, if your SAE plug is tied directly to the battery terminals, it is not key switched. Always hot.
If you already have a Battery tender, and pigtail to the battery, just plug it in.
I wouldn't want my pig tail hidden under the side cover (pulling the cover off all the time can result in broken tabs if you are not careful); suggest you reroute it to the frame back by a rear foot peg and ziptie it to the frame so it is easily accessible (I'd want it on the side of the bike nearest the wall plug you will plug the Battery Tender in).
No SAE plug here.