Video is very short; to ascertain the sound but i assume it is the high pitched squeal? You might try isolating things; by removing the accessory belt or putting tension on the belt tensioner, see if the sound changes or if when the belt is removed, removed goes away.
There seems to be a number of vacuum related parts in the middle of the plastic intake manifold on the 1.6L engine; you might wiggle different parts, trace the vacuum lines, check parts # (8, 9, 4, 3) and put a rag on things, see if the sound changes? This might help narrow down; where the sound is coming from and possible vacuum leaks?
If you don't have a service manual; you should consider getting, the UK version of the Haynes manual, not as good as eRWin factory VW manuals but it does cover the 1.6L engine:
Maybe post some images of the part in question? Some parts are only available from genuine vw only, many parts can be bought with the oem supplier (Pierburg typically made most of the vacuum/emissions parts) and then, it seems in the UK, people are "breaking" their vw's all the time and post used parts ads on the UK based forums and facebook groups. A local auto recycler/breaker/junkyard or ebay could be a affordable source of used parts as well. We hear allot about eurocar parts; as a popular supplier in the uk as well.
You might check with your vw dealer; many new parts are sold as a whole assembly or try to find a good used part for less?
Here in the states there is a 2.0 L engine and the later engine codes/versions had a plastic intake manifold that has a similar valve to your 1.6L and it breaks or the diaphragm gets old, has a tear, which causes a vacuum leak. Unfortunately we have not found a way to repair them and a new or used one is the only way to fix it, I know they are pretty expensive new from voltkswagen.
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