theres nothing much behind the blanks apart from the wires for the fog and half mast switch. yes it is possible, you will need a rotary switch (this would be the simplest way) i will have a look at the diagrams later and see how easy it would be. the idea of dimming them with lights on is so not to be too bright for night time driving, dont know if you have ever noticed but mine reflects off the windscreen, its not really noticable (but would it be when at full brightness?).
yes it is anoying not having a dimmer but they could even be fitted to the blanks as you say uuuummm
without looking i would hazzard a guess and say its likely that the current is reduced to the clocks when lights on by a simple resistor, will see if this can be bridged out, if so then the resistor can be replaced with a volume control type knob. (which would work as you say, as a variable resistor) .