My first BECMI campaign we shared the DMing. I remember no issues with people favoring their own character. A few games since where GMing moved around without issues re the GM's character
A Changeling game where the GM ran a character who was, by any normal interpretation a GMpc. The GM often hit "her" character first if we got ambushed which meant if anyone went down and missed the rest of the fight it was probably the GMPC - so that was good. She joined the character interactions a bit but wasn't a particularly dominant character.
Works. I like to sometimes have my NPCs/GMPCs to ask the dumb question that moves the conversation along. When the party needs to get up a cliff and their plan starts at the top of a cliff and goes from there "How do we get up the cliff?"
Wait, your PCs look like That???!!!