Just to clarify the terminology, none of this actually mutes or un-mutes anything. The Comp Tool (or the little box - they’re the same thing) selects which Part on the different lanes is currently active. But the non-active Parts are not muted. You can see this if you use the arrow tool to drag an active part to a different Track. Another part on a different Lane will become the new active part - no un-muting necessary.
Heck you can even mute the active part and no sound will come out even if un-muted but not active Parts exist.