If picture quality is important to you I don't recommend most of the 12 volt TVs. The fact that its 12 volt should have nothing to do with the picture quality but the manufacuturers must not focus on that because it does. Even the high end 12 volt TVs can't compete with the picture quality of the 22" Samsung we use.
If you want it to run on 12 volts, as long as the brick power supply is designed to provide between around 12 volts to 14 volts, a generic 12 volt power cord with a 2.1mm "universal" adapter should work fine. Ours does.
Other bonusus: bigger screen, thinner bezel, and usually significantly cheaper.
Hmmmm, I have noticed in many reviews of 12v TVs that people complain about viewing angle and sound quality. I may have to look into this option. Thanks.