Good question, however, more information would be helpful. Is this question based on a real life situation? If so were your forced to park on a hill (i.e. Some kind of emergency situation), were you unhitched? How big a hill? I'm guessing if you are wondering about pulling the break away switch you are unhitched?
For whatever this comment is worth: We've never parked, hitched or unhitched, on a hill.
Trailer: "The Trailer", 2nd Gen 21' & a 2017 Tundra CrewMax in Blazing Blue Pearl
If you're thinking of pulling the breakaway cord, I'd suggest getting some extra plastic pin bits for it. Least that was the suggestion my instructor gave me for when I test ours. that way, if it breaks, I have a replacement piece as otherwise it won't work.
The breakaway switch is designed as an emergency device. It puts the trailer's 12V battery (assuming you are disconnected from the tow vehicle) directly on the brake magnet coils, drawing 3-4 amps per brake continuously. This will overheat the coils in the brakes & quickly drain your batteries.
Use your chocks, or leave the trailer connected to the tow vehicle.