Although now not a caravanner any more, I used to be and have wired the sockets on a number of cars.
The fridge supply should only be live with the engine running, so as not to give excess battery drain. You can buy, as I originally dig, special relay boxes for the job. However, as an electronics engineer I baulked at the prices charged, and subsequently fitted a normal car rely (I have plenty spare from scrapped acars). This is wired so that the coil energises only when the ignition is live.
The wiring to the contacts of the relay have a feed from the normal +12v (ie live battery) via a fuse - as you suggest 20A or maybe 30A, to protect the load on that circuit. So having now got a switched (via ignition) feed, this is then wired to the 12S socket.
Stewart
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