I'm not sure what your exact question is---but there is definitely an "art" to Piano/Conducting. There's a lot of head nods and "sniffs". You do what you can---but if you've got good musicians and you're clear (even if it's the smallest eye twitch) it can work.
head nods, sniffs, play the left hand and conduct with the right hand, counting aloud (sometimes the band is all on headsets so they can hear the conductor if they can't see him/her conduct) - theres lots of ways!
Those musicians are such pros, they hardly need any conducting at all. The only disconnect might occur with the actors onstage. I am familiar with the use of prompters in opera, is it done on Broadway also? They provide an invaluable service in many ways.