I have rebuilt a couple of Ampico Players with these little pneumatics.
They were only on Model "A" systems from 1927 and 1928.

They were called a sustaining pedal compensator, and they are mounted
on top of the bass and treble spring pneumatics and are actuated
directly from the Sustaining Pedal valve.

Full details that cover use of the combined A/B test roll (test #29)
and reference to number 23, Illustration 3A, page 8, 1923 manual,
can all be found in the book, "Rebuilding the Player Piano," by Larry
Givens, starting at the bottom paragraph on page 75 and continuing
onto page 76.

I do realize that this early work in Given's book no longer has much
favor with today's player techs, but when I started my interest in
player pianos, other than a book by White, Larry Givens had the only
current resource available.  While now considered out of date, it still
contains some very excellent information.

Regards
Ken Vinen, Stratford, Ontario, Canada
http://www.woodsvilla.orc.ca/