Okay Riccardo. Thanks for the clarification on the wheel sizes. I don't know if the 16" and 12" wheel speedo drive gears accommodate the ratio, or if the speedometer is calibrated differently. I have no experience with that, and guessing wouldn't be appropriate.
You can buy a voltmeter for $5 or less in automotive parts stores, here in the US (thanks to inexpensive Chinese imports). The positive voltmeter lead (red) connects to the connector wire(s) I described, and the negative voltmeter wire lead (black) connects to any bare metal surface on the scooter, or the negative battery terminal. Turn on the left turn signal, connect the voltmeter to the pink wire at the instrument cluster connector, and see if you get alternating (blinking) voltage at that wire. If you don't, then the problem is not at the instrument cluster. If you do, then you can continue to trace the connection into the instrument cluster, until you find the break in the trace. There are no intervening circuits between the indicator lamps and the instrument cluster wire connector. It's just a printed circuit board trace, as you've stated earlier.
I agree with you, that it may just be a broken circuit board trace or two. It is just as likely to be a problem at the connectors too, because the mechanical connection can oxidize, or corrode, over time (4 years?).
Another caution Riccardo: The color code corresponds to Vespa ET models. The wiring may be color coded differently on the LT50, but the 3 connectors, and the wires, have the same position and function in the ET and LT. It is basically the same instrument cluster assembly, except for the differences already noted.
⚠️ Last edited by addicted on UTC; edited 1 time