First, King Tempo was an imported line that was made in the Keilwerth factory and sold by the HN White Co. These saxophones were first introduced in about 1962-1963. The serial numbers did not follow the normal HN White King saxophone serial number list. So, your sax is most likely a 60's vintage instrument. As for the neck octave pip. Its normal for the tube to enter into the neck by about 1/16th of an inch or so. 3/16ths is definitely more than normal. However, for the issue that you're having, I don't think the octave pip is the problem. The octave pip would not cause a random problem. It would tend to make the horn stuffy or affect response or intonation and it would do so consistently. I would guess its more of a set up issue. I once had a customer complain of the exact same thing and it was that there neck strap was bumping the side Bb key when the horn was in a certain position. The random thing makes it a bit difficult to diagnose without seeing it. Anyway, keep us informed!!