Older (pre-198?) Series basses have a stereo 1/4" output jack where the bridge and neck pickups come out on the two channels. If you plug a regular guitar cable into this jack, you can only select one pickup. In this case, the guy in the video thinks he's hearing both pickups, but he's only hearing the neck pickup. This is actually odd - seems like my basses are wired so that you would only hear the bridge pickup. You know it's the neck pickup because the knob that's changing the volume is the neck pickup volume control. It didn't sound like the tone controls were working on that pickup, so it's possible it's been rewired or it just wasn't obvious. On a normally wired Series bass, you should have heard the tone control effect when he turned the knob "beneath" the neck volume knob.
When he flipped the pickup selector switch on the horn, that's when he started getting the bad noises. When you flick the pickup select one position over, it should turn on both pickups, but the output of the bridge pickup is being shorted. That doesn't normally cause a sound, but that might vary with the amp setup (or this bass might be rewired). This is where he's hearing the noise. Interestingly, you can hear the bridge tone control working on the buzz around 1:09. The noise is changing because the unintentional response of the system is changing as he changes the tone controls.
Assuming this bass hasn't been rewired or messed up, if you plug in an actual stereo y-cable then both pickups should work. Same if you use the 5-pin cable and the external power supply box.
