Whatever makes sense. There’s really no need for initiative. Intent and task takes care of it all rather neatly.
You can only engage one target at a time, but you can be fighting multiple opponents. So use the rules for two-on-one if you are engaged by another opponent while in the midst of a fight.
The archer is disengaged. He’s out of the fight. He can’t see what’s going on. He can’t get a target. And he can’t be engaged because there’s no valid intent/task that’ll allow a fighter to accomplish the feat (without magic, maybe).