Try something like
this.
A computer player's WAIT will not affect your triggers. Use a switch to control when the background music should start playing. Under the human player's triggers, check whether "Music Playing" is cleared. If it is, start playing the music and set "Music Playing." Then, under a computer player's triggers, check to see if "Music Playing" is set. If it is, WAIT the duration of your background music, and then clear the switch after the duration has passed. Since it is a computer player whose triggers are WAITing, everyone else's triggers will continue to run as normal.
Tell me if this helps.