I figured that the small gap between the light blue wire was not intended.
I had a good look over your latest wiring diagram and everything looks perfect to me. I have no further recommendations to make.
The flasher relays that we currently sell are designed for turn signals with incandescent bulbs, since these are the type of bulb that practically all electric scooters have. This reminds me to order some LED flasher relays and add them to our website though.
Installing a small 6 Ohm to 10 Ohm 1 Watt to 5 Watt resistor (or two 1/2 Watt, or four 1/4 Watt resistors) between the positive and negative wires going to the turn signal bulbs should solve the problem though. Only one resistor will be needed per set of front and rear bulbs. The resistor will trick the flasher into thinking that it is connected to incandescent bulbs.
Another solution would be of course to use a LED flasher relay instead of one made for incandescent bulbs. This might slightly lower the current draw when the turn signals were on, however since the turn signals are not on very often it should not make much of a difference.
I will order a box of LED flasher relays this week so if you want to simply replace the non LED flasher with an LED flasher please let me know and I will send you one when they arrive.