I'm a godfather/honorary uncle to a number of preschoolers. They get excited about my visits and mostly prefer to play with me. However, during my longer (8 hours to few days long) visits they will eventually ask to watch TV at some point.
I wouldn't say they are watching TV excessively, or ignoring me. Generally they spend most of their time playing with me, even if TV is an option; and if given a choice between turning off TV or having me leave they would choose to turn off the TV and keep me. I know they prioritize me higher in general. However, they can still get sidetracked by TV for a while, and when that happens I get sidelined. Sometimes I can encourage them to play with me instead, sometimes they turn down my invitation to play to watch TV instead. Yes I could simply tell them to turn off the TV or refuse to turn it on, but I don't like forcing them to play with me when they actively are requesting something else; it's not like they're getting too much screen time when I'm around.
I'm not that upset that they sometimes choose to watch TV, I know they still value me. But when I only get so much time with them I want to do the most good I can to help mentor and guide them during that time, and I feel like I'm not doing much to help them grow as kids when they're watching TV.
How can I get the most out of the time when kids are asking for TV?
That could be convincing them to play with me over the television, or helping to interact with them while they're watching TV so I can still be doing something to guide/mentor them during that time.