Ok, so hear me out as I just thought of this. This would be something akin to a capo and a piano's sustain pedal. It could clamp on to the neck of the stick and allow you to pull off hammer-ons and pull-offs like you would on a guitar, while not having everything go mute as soon as you release. It would use a cable in a sheath (not unlike a bicycle brake cable) connected to a pedal that you would use to engage/disengage. Currently thinking that it would be an open bypass by default, but the moment you engaged it, it would allow the function that you would get with an open guitar/bass string.

I just called L&M in Vancouver (as it's close to midnight in NS), and they never heard of such a thing, so I don't believe it exists, so I am wondering if anyone here has heard of something like this, or would find something like it useful. Just something random I thought of while wondering how well Gojira (lots of tapping) could be played on a stick.

Garry Goodman uses a custom SpiderCapo XXL on his 12 string tapping guitar.
The site states custom sizes for tapping instruments are available:
https://spidercapo.com/products/spidercapo-xxl/

Closest thing to your idea i know of, although of course each string capo must be individually actuated by hand.

Ah. Interesting. I use Shubb Capos, flat wide for nylon string guitar (on either or both sides) and cut the rubber so it only "frets" the strings I want.
Tawdry but workable for my experiments.
I might have to give them a ring, see what they might come up with.
The lowest strings on both sides, I really can't capo them. And I set the capo right over the fret as not to effect string tension.

Bob uses a capo for that very idea. He puts in on his bass strings but I think only on the four highest (maybe the five highest). He cut a guitar capo to fit.

I've seen Andy McKee use a banjo cap to use on only strings 1-4 or 3-6 of his guitar. I recommended to Bob that he give that a try. I don't know if he ever did.

The Spider Capo is super interesting. I saw Antoine Dufour play with one of those and he really made good full use of it (see video below).

The closest I've seen to something mechanical like you mentioned is the damper Emmett put on the NS/Stick which you can turn off so as to be able to play the open strings.