Headrest monitor power problem

Ok, before I get into the problem, let me tell you what I'm working with

1999 Ford Contour with stock battery, and two 5.6 inch Movies2Go monitors, 12 gauge power and ground wire

So, the way I have the TVs powered is there is one power wire for each TV coming directly from the battery. The wire then is fused with a 3A in-line fuse, then it goes to an interruptor switch (a blue glow switch from Autozone) then to the TV. Each TV as well as each switch is grounded on a single wire back to the battery's negative post. When the car is on ACC and the radio is on, I can turn both switches to ON and press power on both TVs, and they will power up. However, when I start the car up, the switches stay glowing but one of the TVs goes out as if it's not getting any power. Any idea why? Thanks for the help, if you need more details let me know

See, I know it isnt the switch because I had the same problem before when I had both TVs running off of one switch. I also dont think it could be the switch, because how could the switch not work ONLY when the car is running?

Another detail: when the car is running and the faulty monitor is off, if I turn on an accessory like the headlights or interior lights, the screen flickers a couple of times like its getting a little power jolt. But, it still doesnt come on