What should be avoided is lots of flickering, unless you are going for that "Poltergeist" vibe (though today you don't even get static over a broadcast channel...)
The light from a TV has some random flashes, changes in exposure (and color, to a less degree) as edits happen in the program, and slight shifts as bright objects move across the screen. And generally you go for a cool bias to the light because TV sets are daylight-balanced in a usually tungsten-lit night interior, though if you are going to be cutting a lot to the image on the TV set and it is color-corrected for normal balance, then the light coming off of the set can't be too blue-ish.
I find that the best method is to shine a soft light at the actors and randomly wave my hands & arms or a thin flag in front of the soft source -- that way I can speed up or slow down the flashes and shifts randomly, though it takes someone who has a good sense for this if you aren't doing it yourself. Sometimes if I can sit below the soft light I can wave both hands and arms like someone waving flags at a ship, although the downside to this is that an actor will find it distracting -- I had one actor burst out laughing watching my hand waving.
In that case, I'm more likely to get behind the diffusion frame to be partially hidden, or to use two lights through one diffusion frame, one flicker boxes with different tempos, one barely changing, the other changing faster, both random. Or one light on a flicker box but the other on a dimmer, just fading slightly up & down randomly.
But I think the hand or flag waving looks more natural because if you slide the flag from side to side, the soft light shifts from side to side as if something was moving on screen. A combination of all of these tricks can work.
The other option with the new high-sensitivity cameras is to use a big TV with bright scenes playing on it, with lots of edits in the material, and use the actual light of the screen, or get a bright video projector and project the image onto the actors, softened by a light diffusion frame, maybe also thrown out of focus. Again, you'll want to select images that are bright with lots of cuts, like a daytime action scene in a movie.