> it would probably be similarly effective for personal protection.

Unlikely. The virus containing moisture particles are pretty large and easy to catch when you exhale them, but they rapidly dry out and become very small - small enough to make catching them much harder.

I would assume that a neck gaiter would be very much like a face mask on that front, though obviously much less effective because of not being designed / tested for the purpose.

More info here - I recommend having sci-hub to hand, too.