Don't know if it would be a good idea to undervolt things like cathode tubes...I've heard of many instances where they tend to get really hot and sometimes catch fire as it is muchless changing the voltage and brightness regularly.
You might look at the Sunbea Rheobus as it's a nice controller with 20w per channel which is higher than most fan controllers I've seen. Not sure if they use variable resistors though
Basically you would need a variable resistor and connect that onto the power cable going into the inverter on the 12v line
With the rheobus you should simply be able to take a 4pin to 3pin adapter and plug that straight into the controller.