There should be 4 wires to the signals from the switch if you have front marker lights that switch off when signalling. The front and rear signal lights on each side are wired together, so there must be a wiring problem if only one works - wires are light blue for right and green for left, I think. The front marker wires should be light blue with white stripe (right) and green with white stripe (left), some harnesses have plain color wires with a white plastic ring near the connectors.
First, fix why both signals don't light when the wire is connected to +12 battery power.
The signal switch does a lot if the bike has front markers. When activated, the signalling side's marker power is disconnected and its signal wire is connected to "flashing power" from the flasher, the grey wire.
Test that all the lights work as expected before digging into the switch. It is complicated with several moving contacts, detents, and springs... be 100% sure it isn't working properly before opening it.