In other words, when you focus on one hand (say the fret hand) and look at it as well, the other lacks signals to gain coordination, dexterity and equal responsibility, so it relies on reflex by the hand getting the spotlight. The next time you play, don't look at either hand and see how you do.......
Split the Brain signals and both hands will know what to do. It reminds me of an old Budgie tune I listened to long ago "Crash Course in Brain Surgery"...
Budgie Kicked.....................................