Going further on this aspect, if you wanted a static color for multiple buttons that was a combination of two LEDs (say, purple), could you do the same thing, but just daisychain the red wire and daisychain the blue wire?
Yes. If you like how it looks with the channels at full strength you could even hook them all to the same daisy-chain ground.
That's why there is a question mark next to "Variable Resistor" in the diagram.

*** Depending on the RGB LED, you may still need a current limiting resistor. ***
Test max-rated current flow for each color channel using a multimeter inline that's set to "mA".
- Use a 500 ohm or 1k variable resistor.
- Start with it set to max resistance.
- Slowly reduce the resistance while watching the multimeter.
- When you reach the max-rated current flow for the LED, switch the power off.
- Check the variable resistor's resistance.
-- If the variable resistor reads something like 180 ohms or 220 ohms, you'll want a current limiting resistor of that value or slightly greater.
-- If the variable resistor reads close to zero ohms, you don't need a current limiting resistor.
- Different color LEDs drop different voltages and therefore need different value current limiting resistors.
i.e. A 20 mA red LED that drops 1.9v will need a larger value current limiting resistor than a 20 mA blue LED that drops 3v. The red resistor has to drop 1.1v more than the blue resistor.

Scott