1. Black box is high voltage ignition coil (Bosch)
2. Yes, if ignition coil is not connected, you get no spark & engine does not start.
Bosch high voltage ignition coil needs both spade terminals connected to it.
- One spade terminal goes to magneto points/condenser (Sachs blue wire usually)
- 2nd spade terminal goes to ground which can be frame of moped or outside engine (Sachs brown wire usually)
3. If that hanging Blue wire is from stator magneto points/condenser, then that should connect to spade terminal on Bosch ignition coil.