The cap can swivel back and forth, no worries. But it must stay on!
The clipping bit inside the rubber boot of the spark plug cap may be chipped.....preventing a nice solid "click" onto the spark plug top.
These caps are not expensive, and its connecting wire to the coil...both parts are not expensive.
For now, get the cap on there as best you can and get on home!
At home, if you have an old spark plug
...try connecting it to your scooter's plug cap. If it won't go, then you'll know...need a new cap. They just screw onto the wire most times.
Good roadside sevice find....well done!
Stig