Well ... as an AA GA from long ago, I can say what their rules were back then ...

There was no such thing as "list for the jumpseat". FAs and Pilots, when flying non-rev (IE: personal travel vs "deadhead" which is company travel) are allowed to ride in (their respective type of) jumpseat ONLY if all cabin seats are full. They "list" for the fact that they desire non-rev/standby travel on the flight, but they do NOT "list" specifically for a jumpseat. If memory serves me right, if assigned a jumseat then non-rev service charges were waived ... thus they could not request jumpseat to avoid charges, they would be assigned jumpseat if it was the only option.
They do not need to be in uniform to ride jumpseat. Vacationing Pilots & FAs are (practically) never in uniform. Commuters (again: different from deadheaders) very often are.
I have had crew members graciously, when they were next on the standby list, offer to ride jumpseat to allow another (lower on the list) non-crew employee to have a cabin seat.

If you're in uniform, you may not drink alcohol no matter where you are seated. To passengers, you look like an employee, possibly headed towards duty.
If you're assigned a jumpseat, you may not drink alcohol no matter what you're wearing. You're sitting in an official crewed position; it makes no difference how you "appear" to passengers, you may not drink.
If you're seated in the cabin and are not in uniform, then not only do you appear to be just another passenger, you actually are one. Enjoy your flight, keeping in mind that if your selected beverage/meal/etc is running short, you'll be the 1st to be asked to switch.

As a Gate AAgent on 2nd shift, at 11pm after 8 hours on duty, we were all ready for a drink at our favorite watering hole (and trust me ... said spot was definitely off airport property)
Very few of us carried a change of clothes. But we had to remove anything with the name/logo. For us guys, obviously the badge, name tag and ties were off ... but also the belt because the buckle was AA's stylized Eagle. ALL types of logo had to be off.

As for the ID badge still being worn ....
I think 9-11 changed the philosophy on this. My post 9-11 days at AA were all behind the scene HDQ type jobs, so this is just my theory.
In my days at the airport (pre 9-11) my ID was just a card I carried in my wallet. It was my uniform and door keys that gave me access to everyplace I needed to be.
9-11 changed all that. Uniforms no longer proved anything. A key that could open any AA door (at my access level) system wide was worthless. The new TSA decided employees had to go thru screening.
ID's were needed so much/often that they came out of the wallet and onto a lanyard. I think that out of habit, employees today simply keep that lanyard handy at all times they're doing anything airport/airline related.