Here's the inside of the clock. The smaller board in the top half contains the 74141 Nixie driver chip, and a Supertex LR645 which regulates the tube current. The red wires connecting to that board are an original part of the counter module, clipped near where they connected to the module's edge connector and routed through a hole drilled in the bottom of the module. This gave me all the connections needed to drive the Nixie tube at very little effort, unfortunately the connections aren't direct - there's a series resistor in each line, and pull-up resistors that would have overloaded the driver chip if it had to fight them. I replaced all these with suitably low/high values, using old-style carbon composition resistors to preserve the look of the module.
By far the most difficult part of building this clock was the clear plastic cover! I built a plastic bending jig using the fuser roller from an old NEC Silentwriter printer, and bought a clear plastic sheet - the original plan was for a 4-sided cover, completely enclosing the counter module except for the end with the Nixie tube. Unfortunately, the plastic I bought turned out to be unsuitable: I could not find a temperature setting that would bend it without actually melting it, the results were quite ugly. (I've since had better luck with some different types of plastic, although I didn't have a large enough piece of any of them to make a cover.) I was just about to start calling around to see how much a professionally-made cover would be, when I visited a local bookstore that was having a going-out-of-business sale. There, among the various store fixtures that were being sold, were some 3-sided clear plastic thingys for 25¢ each. I don't have the slightest idea what the store used them for (and neither did either of the cashiers), but they're amazingly close to a perfect fit over the module. They're not as long as I wanted - even two stacked end-to-end wouldn't cover the entire length of the module - so I had to change my plans a bit: I used one to cover the immediate area around the Nixie tube socket, and cut some traces on the bottom of the module's PCB to completely isolate the exposed areas of the module from the high voltages in the covered area.
I considered the idea of lighting the tube filaments just for effect, even though the tubes weren't actually doing anything, but gave this up when I realized that it would increase the clock's power consumption by a factor of 20. I'm not sure I could have fit a sufficiently hefty power supply within the 1" high project case that forms the clock's base.