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When that thing is in the reservoir and the cap is sealed, it forms a system like an expansion tank:
So, that rubber piece would essentially keep the air and fluid from mixing. I wonder if there is some sort of condition (under acceleration) etc. where fluid can slosh in there and air could be sucked in to the system, necessitating this barrier between the fluid and air volumes?
WSSix99 is correct. If you fill the reservoir at the level where the fluid comes up the top when you put the insert in, it will expand and contract as needed during clutch use, and not introduce new air and moisture into the system as the level changes. .
Yes. That rubber bladder "blows up" like a balloon when the reservoir is emptied when one presses the clutch pedal and a vacuum is created in the reservoir. This keeps the air and the fluid separate and keeps air from being sucked into the line, which we worked really hard to bleed out of the system when we last worked on the hydraulics.