My wife bought a folding shopper bike a while ago. We like to ride at night from time to time so lights are a must.
Unfortunately due to crazy construction the bike has no bracket to mount a light, no area really available to mount a light and if ya tried mounting one in the normal place the ********** basket is in the way.
To compound things the lights the missus has are the silicone Frog Light type - this means that clamping is done in the horizontal plane, here is how we managed to solve our issue.
Step 1: S1
Step 2: S2 - you will need
2 - plastic pop bottle caps
2 - lengths of old bike inner tube - one about 10 inches long, the other about an inch
1 - Light
1 - Bike
Step 3: S3 - Assemble
Step 5: S5 - Shaft
Put the light up against the shaft with the cut out facing inwards.
Wrap the inner tube around the metal until the ends meet.
Push the short length of tube over the ends of the longer like a rubber band, effectively stopping the light from falling