Devo;
Warning, I am no gear head. Know little about cars. Wouldn't a fuel pump relay be better suited to being on for extended periods?
That still leaves the AC being switched issue of automotive stuff.
Furnace controls often use 12 or 24 volt activated AC relays. Switch AC and use low voltage ac on the coil. These should be OK on same voltage DC. I think.
Just off the wall thoughts.
Tom