Three months? The Airstream batteries will be dead from other parasitic draws long before the jack does it.
I never thought about it, but you're right, since it has a remote, the receiver is always on standby.
Yes, a battery disconnect is the best mod I've done to save my sanity. The jack power goes directly to the battery, but since my switch uses the negative cable, it also disconnects the jack.
I made the mistake of troubleshooting the jack one time. I expected to take off the cover and find a motor and gears, maybe some set screws. What I found was a normal looking head outside packed with electronics inside.
But if my Husky 5000 died today, I'd replace it with the same unit!!