Is there a specific name for those convenience store roadside billboards that have that flashing arrow on top… and the letter tiles that you can advertise on? you know the thing that lights up… says… KARAOKE TONIGHT THURS $1 Draft Beer…
help me out here. it’s a brain fart i guess.
'Round these parts, we’d call that a ‘reader board.’ Don’t know if that’s any kind of official term, though.
Do you mean a
Is it not simply a Marquee?
A marquee is a big tent, duh. 
I’d call it a marquee if it’s permanent, and a portable sign if it’s the kind you can move. In a lot of places one can only have a portable sign out for so long, per city ordinance, FYI.
When I was in outdoor advertising we always called those attraction boards or 'traction boards.
OOPS hit reply too soon. They are usually classified in ordinances as trailer signs and are heavily resticted in their use.