I can't diagnose from here but introduce more of the simple or obvious points to eliminate. There is no place to begin sort of speak, but to hold the imaginary winker assembly in hand:
1. Wire In... is the hot side.
2. The illuminating LED's... is the winker itself. As the wire continues connecting one LED after the other, there is no break in the chain so the wire continues showing joy at this point.
3. Wire Out... is the ground side.
The diagnostic tree goes something like this.
a. Connector Not Connected: Let us eliminate this because the connectors do show current flow obviously being connected.
b. Wire Out Of Connector: If you think about those 2 wires can still illuminate the winker, it's logically not this either; said in simple terms.
c. Short To Ground: That's basically it for the wire in or wire out scenario. Either the unit is broken showing a break of flow, the hot is grounded direct, or the ground is not connected [well]. So it's this one... Bad Ground. Why? The connector is connected that shows current flow. It sure is not disconnected, right? It sure is not shorted to ground blowing fuses, right? So it reverts back to 2 wire ends. Who's [ wire side] does not have a solid connection.
Note:
The winker photo; look at the vertical lines above the winker base that butts up against the fender. Is that rattling up and down or is the photo deceiving>> having those lines above the winker? Sometimes a winker base acts as a ground source.