Assuming your term 'ADAPTER' is a small wattage power Inverter...
Be mindful 8A is not a lot of power... If you blow the internal fuse by drawing more than 8A then your TV ANTENNA is not going to work.
I elected to wire my POWER INVERTER directly to my battery source and not use the ANTENNA WALL PLATE 12V receptacle...
I also will not run my electronics including a TV set on anything except a PURE SINE OUTPUT POWER INVERTER. Most of the small power inverter that come with a 12V socket plug are modified sine wave units. A lot of electronics including the TV sets do not do well with modified sine wave inverters... Anything with motors like small fans will go up in blue smoke most often being plugged into a Modified Sine wave Power inverter. The motors gets very hot when being used.
I elected to go with a 600WATT PURE SINE WAVE Power Inverter and have it mounted close to my battery bank. Then I run a multi-head 120VAc drop cord from the Power inverter to the home entertainment area where I can plug into the multi-head drop cord. Works great for what I am doing.
I very seldom need more than 200-300watts and my 12VDC Power Drain is around 20-25AMPS DC current during the evening with watching TV and playing with my Ham Radio/Computer items...
I got the AIMS 600WATT Power Inverter from AMAZON several years back for $159.00 and it has worked great ever since... being PURE SINE WAVE I never have to worry about anything going up in 'BLUE SMOKE'...
This works great for me - I'm sure others do it differently haha.. My 600WATT Power inverter is sort of my basic emergency Power Setup that is always ON. Works like a Backup UPS unit you find for home computer setups... When SHORE POWER drops out everything I have plugged into the 600WATT Power Strips continue to work for me... I have this power strip mounted on the back of a cabinet top close to the home entertainment area in my POPUP .
I usually make it through the one day/night run off my batteries with the 1-2A Parasitic drains from monitors etc and from using my Power Inverter drawing 20-25A DC current from 5-10PM in the evening. I watch my battery bank real close to see if it ever gets down to around 12.0VDC on my DC power Panel. Then I stop using the batteries until I get them charged back up to at least their 90% charge state using my 2KW Honda Generator the next morning during breakfast.. this usually takes around three hours of generator run time to get from the 50% charge state to the 90% charge state. Then I am good again to make another day/night run off my batteries... All of this takes good planning in order not to do harm to your batteries.
Roy Ken