Here's a render of the gag with most of the rest of the muzzle taken away, as well as a cross section diagram.

The gag has a plug to close off the feeding tube. This is to prevent saliva from dripping out as well as to further reduce the noise an inmate can make while wearing it.

The feeding tube in the middle has an extra feature, a spherical cavity about 4 cm past the opening. This is to accept the gag plug, which is made of a very stiff rubber and will, at rest, have a spherical bulb at the end to match the cavity.

Plug is handled by a robot arm with a suction cup tip connected to a vacuum piston. Prior to insertion, piston will retract pulling a strong vacuum inside the plug, causing the bulb to contract. Suction also secures the plug to the arm. Once inserted, the piston extends, releasing the vacuum and allowing the bulb to expand, filling the small cavity and locking the plug in place.

This is meant to work with no lubrication provided all surfaces are polished. Actual dimensions would be worked out in the prototyping phase. Actual filler material for the gag will be worked out later, or left ambiguous. As long as it is some kind of low density liquid or gel (NOT a gas!)

The outer portion of the plug is much less substantial than the one I used to draw, it no longer looks like a pacifier and is now simply just round.