Modern Vespa

My left turn signal isn't currently working, neither on the front or back. The right signal works just fine, so I imagine the problem is somewhere in the wiring coming from the switch?

When I opened up the front, I noticed a white wire with black stripe was frayed, so I cut it and reconnected (you'll see the butt connector in the photo) but it didn't help. No other electrical problems as far as I can gather.

Anyone got any ideas?

Also that connector just off to the left of the picture with one pink, one white/blue wire doesn't go anywhere but I did a little digging and as far as I can tell it's not supposed to, but please correct me if I'm wrong!

Have you tested the switch itself?

I think you're correct about the extra connector. The wiring diagram at https://manuals.wotmeworry.org.uk/Vespa/LX150/LX150%202009%20wiringdiagram.pdf shows it as a "spare". It looks like the pink wire is the same circuit as the LH turn signals, so you should see 12 volts from the pink wire to ground when the turn signal is on. This may help troubleshooting. Good luck.

Since you've already taken it apart, you might want to consider switching it to the European style signals, which means you put amber bulbs in the light fixtures on the body of the bike and run the turn signal wires to those. Then take the stalks on the handlebars that break, off the bike.
If you find you need to have someone in the business fix it, I know a couple of very good independent shops or repair people in NYC. PM me for contact info.