I'm not sure what specific plug it should have, as my documentation is mainly focused around ETZ models, which do require the B7HS.
It's quite likely that your little TS is indeed a B8HS, but it's worthwhile looking at manuals. I don't have the TS125 Haynes, only the ETZ. I'm sure someone else on this forum can provide, and I can then also mirror the data on my own server to provide myself when required by someone.
I haven't got first hand knowledge of the TS, but I the clocks have two lamps in them which give tell tales for 4 particular jobs. I am unsure which is which, but I believe that one of the lights is a neutral indicator, but when you turn on the indicators it flahes, whether or not you are in neutral, I believe it also stays on when the bike is discharging from the battery beyond the ability where it could reasonably sustain the engine, but that could also be the dual job of the high beam indicator if said bike has one. I'm not too sure. Regardless, I double checked and I do have an official service manual located here in PDF format, which includes all you need to know even about the ignition switch (but unfortunately it states an IFA specific spark plug not an NGK equivilent):
ftp://blurredmanswebsite.ddns.net/Vehic ... Manual.pdfIt also has better detailed information as to what idiot lights do what and how, instead of my guessing above.
The key in the lamp is also the lamp switch. In the default position of being off, the key enters the lock in the position of around 5 o' clock.
Ingition on (with no lights) is acquired when flicking the key clockwise to 6 o' clock, the next position over at 7 is side lamps, and the last position 8 is main beam, where as you have found out you can control whether the main beam is dipped or not at the switch on the handlebar. Also to note, the side lamps (or parking lamps also known as) are at the 4 o clock position. You cannot /should not be able to take the key out of any position other than 4 and 5.
If the lights are left on with the engine not running it does not take very long at all for the battery to go flat at all, as the main beam is actually very powerful and the coil will also be receiving current which is unspent, which is also dangerous for the coil as it can burn out. This is why cars have accessory slots for radios.