Would this same theory apply to a full time LEO working a second job that prohibited weapons?
BC
That's an interesting question actually. There is a national CCW law that covers full time LEO's. But it enjoins other jurisdictions to allow an officer to carry concealed within their jurisdiction if they choose. It's not actually binding on land owners or lease holders.
Even an on duty officer must leave a privately held space if the owner/lease holder doesn't want them there (assuming they aren't investigating a call or crime there).
A public space would have less options, as they've opened themselves to the public and the officer's duty is to protect the public.
Is the officer within their jurisdiction? They may have a requirement to carry off duty if their dept. says so, and respond accordingly if they witness a crime.
I really don't know the answer to that one, but I doubt a full time officer would take a part-time job where they were told they couldn't carry, especially within their jurisdiction. Many departments control part time job assignments to ensure their officers are available and fit for duty, and to avoid any potential conflicts of interest.
Perhaps a FT officer will respond.