The feed to the fridge is never permanently live for obvious reasons. It uses pin 10 which will only supply current with the engine running .We had the Jeep done last year by a Nationwide specialist company, but stating we did not require the permanent feed for the fridge has raised concerns. We seldom connect up with the engine switched off .
I would normally reverse up with OH guiding me, then lower hitch onto towball. connect breakaway and lastly the electrics. ATC does its thing and green light is on.