BBPhil, sorry not to reply earlier. You've clearly got it, and it works so I guess there's no need to explain it again!!
You don't switch the speedo on because the voltage it is seeing from the receiver pack is then 'opposed' by the voltage it would see from the internal regulator. Something has to give, and it is usually the smoke capsules fitted as standard to every electronic device!!
Dodgy, you are spot on. It will work with a 1S cell as well. There's no issue with straining the voltage regulator as the Tekin it will take 3S fully charged, and with a 1S cell and a 2S receiver pack the input voltage to the speedo regulator is the same as that coming from a 3S pack.
This is the reason Tekin like this system with their speedos. They know their voltage regulator will take the 3S charged voltage (12.6v) and output the correct voltage to power the speedo. If you put 7.2v straight into the receiver (8.4v charged) then it by-passes their voltage regulator and the speedo control circuits see that voltage directly, and it is a bit high for some components and can cause issues.
The only speedo I know it works for is the Tekin. I don't know if it works for any other speedo so you try it at your own risk. In order to know which receiver pack to wire in check the voltage rating for the speedo. If it is 4v-9v then it is 2S only - it may also say 2S or 4-6 cells - so you can only connect a 1S receiver pack into the line. If it says 3S, or 4v-12v, then you have 3S capability and a 2S receiver pack is fine. However, you have to know what line the switch is in.
In the case of the Tekin, it is seeing the input voltage directly from the main battery pack, so adding in the extra voltage to support the 1S main pack works. Not sure if it would work for an LRP or HW, etc. HTH