I agree with the 12v when on answer.
As a clarifier - the actual speed sensing unit is located in the speedometer. When less than about 17 mph (don't remember the actual number), the "speed warning unit" (which is just a relay) is energized and its contact closes. This relay contact is in series with both the solenoid valve and the "changing relay". The changing relay is controlled by a transmission switch - and is energized when in Lo or High (or 1 and 2).
If your Lo/High (or 1/2) lights are working, then your tranmission switch is good.
It may be hard to hear the click - since your shifting at the same time. You may be able to feel it, though.
It may be easier (to hear it click) to locate the "changing switch" wires (comes out of the left side of motor heading towards the left side cover area) and with the bike in gear, ignition on (set your handlebar engine shutoff switch to off), disconnect and reconnect the changing switch wires. The solenoid should be heard clicking. You have two wires, one for lo, and one for high.
I tested my solenoid with a 9V battery before installing my carb set this spring. It is easy to hear it that way, too.
No clicking? Other than wiring, check the speed warning unit and the changing relay.
At the changing relay, with the bike ignition on, (set your handlebar engine shutoff switch to off), you should have 12v across the green and the green/black wires.
At the speed warning unit, with the bike ignition on, (set your handlebar engine shutoff switch to off), you should have continuity across the green and brown/red wires (my schematic is hard to read - it looks like brown/red).