In the first photo , is the device I have circled in red , part of the brake booster vacuum system ( with the zip tie on it ) ? I do not think so ?
In the second photo , the area circled in red appears to be where the vacuum hose attaches to the booster . Where does the other end of the hose attach ? Should be at the engine , at a vacuum source . Intake manifold ?
Also , as a shot in the dark , have you thought about replacing the rubber hose ? Should be fairly inexpensive ?
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God bless
Wyr