I was checking the vacuum on my car (300D 80) so 1st I disconnected the hose from the pump and the vacuum was fine. I then reconnected the hose to the pump and then I checked the small nipple on the hose it was still pulling good vac, same with the second nipple. I then checked the end which goes to the booster and the gauge was going BACK AND FORTH BACK AND FORTH. Is my booster vac hose bad? and what is that in the middle of the booster vac hose that round half black/white thing? Is that piece bad? And my brake pedal is very stiff.

Another thing is that my car won't shutoff. My car had been sitting for a few years and just before that had my ignition repaired. So while iI was testing the vac i turned my key off and blocked the single vac line that goes in the YELLOW door lock check valve and it shutoff instantly. What does this mean? is my shutoff valve good? and perhaps the guy who worked on the car switched the vac hoses going to the ignition?
Im new to these cars so im not sure what is wrong. Thanks...

That demonstrates that the shut-off valve works and suggests a vacuum leak(s) in the door lock system which is "stealing" the vacuum needed for shutdown.

where should I look first to try to solve this problem?