I think it's really important that you not cloud and color it all with pressure and tension. That is, you don't want to make toiletting a situation where she has somethign to push back against. It doesn't sound like she is resisting, just forgetting when she's very involved in something. That's completely normal!
I wonder if she also perceives the accidents to be a problem -- that is, is she upset when she does have an accident? If so, you can use that as your starting point -- "I'm here to help you not have these accidents. And here's the plan: before you start do something that you especially love, we need to try on the potty, and then every 30 minutes I'll come and remind you to check in with your body and see if you feel the peepee." Use language that's authentic to you but the idea is that you SHARE the responsibility -- you're there to help her dial in and notice her body, you're going to support her by giving her reminders, but you're also going to trust her if she checks in and says she doesn't need to go -- it sounds like she knows the cues when she's not absorbed in some activity or TV show.
If she's not disturbed at all by the accidents, then that approach might work less well because she doesn't share your motivation. You might need to set it all up differently.
I think it's important to reason with her and explain what's going on, so that when she's asked to try or to check in about her body she will already have had a "heads up." It's easier for her to cooperate if she's prepped.