The fourth button is a silencer and, most likely, part of the problem.
The intended use for the fourth button is to skip over parts of the
roll as it is playing, advancing it ahead silently.  The button is
cutting off the supply to the pneumatic stack.

Somewhere this has device has been erroneously connected.  I do not
have any tubing diagrams, but suggest one starts at the stack cut put
and work their way back.

First, does the silencer button work?  If not, it probably has been
connected incorrectly.

Bruce Clark