12v outlet for TV, the one with a switch for the antenna Amplifier ?
it serves (2) purposes, it supplies 12v for a small TV,
and it injects 12v into the coax going to the Amplifier in the Antenna head
you very likely have a bad antenna amplifier
water has gotten inside and corroded the board
or something has happen to the coax going to the antenna
i think your mysteries are solved replace the antenna coax and antenna head ( of course disconnect the coax on both ends, then check with the ohm meter, should be NO continuity aka open circuit, resistance should be infinite, any actual ohms, reading the cable is bad
power use for the amplifier is in the Milli-amps
10 amps would melt that coax
you might have already disconnected that outlet, which means the wire leading to it has melted/did melt before you got to it, which is where your 10 amps was going