Dimmer Schematic
Here's what I've come up with for the dimmer.
As to voltage. Most diodes (silicon, LED) only need .6V to turn on.
As you increase the voltage they turn on harder, draw more current.
In an LED that means getting brighter. That's why this fixture has the little
resistors on the board. To limit the current being drawn by each LED so it doesn't destroy itself.
I found this fixture stops making visible light at about 7v. At that voltage although you can't see any light, it still draws 10ma. At 9v it's bright enough that if I forget and let it turned on, I'll see it.
So here's how the circuit works.
The 7809 tries to regulate whatever comes in to 9V. By putting the pot in the ground lead, you can shift it's reference upward. Raise the resistance there, output voltage rises accordingly. On the bench I find with 2.5k (2500 ohms) it won't rise above 15v or so. Even with 25 applied to it. Safeguarding the light fixture. The caps are there to stop the 7809 from oscillating (something the 78xx and 79xx series will do).
What you end up with is at one end of the controls range the center pin is grounded and you get 9v. As you turn it, the output rises. And the LEDs get brighter. Viola... an LED dimmer.
If you build this, remember the pot has three legs. One of the outside leg needs to be shorted to the center. Which one decides which direction is brighter or dimmer.
If my memory serves correctly the 7809 will supply 1 A at 9v.
The fixture draw about 35 ma (.035 A) each.
You could do this with just a pot. But all the current of the fixtures would be running through that pot. This way the pot should last for a long time. Also the 7809 has it's own thermal and over current protection.
And of course the usual disclaimer that I ain't responsible if you burn something up applies.