If you put it in your jacket, secure your jacket. Some scumbag took mine off my bike in Johnson City TN. That jacket also had the keys to my travel trailer in the pocket. Bastid...
If you put it under the seat, have a generic key made for your normal keyring that is likely in your pants pocket to unlock the seat (and gas tank and bags). That'll lock up your fob and make it convenient to unlock the rest. I have a generic key and a Givi key on a ring in my left jacket sleeve.
strange you mention that, where were you when you left your jacket unattended???
I make a point of removing everything from my Stich that is "stealable" and stuff it in a small fanny pack when I leave my stich on the bike... and I only leave it on the bike
when in sight, at a COG function...( because everyone knows better, and doesn't want to test this old man's "punch Powah" (which excedes the Mad Powah of KiPass by 3000x)...
If I leave my Stich on the bike anywheres else, I run a very stout Master Cable lock thru the sleeves, and leg on the stich, and over the seat and thru the rear rim on the bike, for secure storage... if they want to cut the stich apart to steal it, i guess i get a new one...
I also keep the keys for my rear trunk, and my locking Garmin mount, and even my trailer locks, attached to both fobs, which are never left to someones pilfering hands.