a few games don't have a specific "start" Button but use Button 1 for player one as the single player start button and the Button 1 for player 2 as start for a two player game, have you tried that yet?
Hit Tab
Look at P1 Button 1 (that should start 1 player game)
Look at P2 Button 1 (That should start 2 player game)
I'm running an older version of Mame and like you said there's no listing for player 1 start or player 2 start
but I checked it out and the above works on mine
oh by the way you can configure both your coin button and player button to do the same thing just don't hit the start button by accident when your playing
because it will still act like the player button and rotate the piece, but realistically there is not much chance of that happening