As far as I know, the early mk2 like yours has a relay fitted to the uch
behind the fusebox on the dash.
By rights it shouldn't be putting a feed to the rear screen until the button is pressed.
The relay could be stuck or the button faulty meaning it's giving a live as soon as ignition is on.
That doesn't really explain why it's blowing the fuse unless you also have a short in the wire to the screen as well.
Not sure if the circuit goes from fuse to relay or other way round.
It would be worth unpluging the relay in the first instance and seeing if it still blows the fuse.
Might be able to piont out the relay if you can pull down the uch
and post a picture of the relays on it.