Brian: You can find these ultrasonic cleaners in supermarkets from time to time; optitians use them for cleaning glasses; the supermarket types are rather small but large enough for "cleaning" tubes like the Z566M. They only cost $20 or so, and I have found them very helpful when trying to clean something with a lot of dust and grease on it.
I have never tried it with Nixie tubes, though, I am afraid of the glass breaking under the vibrations.
I might see if I can find a cheap cleaner then... Probably a good idea to try it out on a few cheap tubes before I try cleaning something more rare. I've never used one so the thought of it damaging the tube like Micah suggested never crossed my mind before.
Here's the relevant parts of an article about ultrasonic cleaner damage, from the Zenith Ultrasonics website. The short of it is, nixie tubes are probably the last thing you want to put in an ultrasonic cleaner...
Ultrasonic cleaning systems, under certain conditions, have the potential to damage components being cleaned when the material of construction is sensitive to ultrasonic cavitational attack, or when the material itself is prone to vibrational damage.
The damage produced on components sensitive to cavitational attack appears as very small comet-like spots which cover the entire surface. A pin-hole of surface damage is evident, and a "tail" is present which drags out from the spot in a specific direction which indicates the blast direction of the cavitational attack.
The distance between neighboring spots in the amount of time required to damage the component is determined by the ultrasonic frequency in use. The higher the operational frequency, the longer it will take to damage the product since higher frequencies produce a less aggressive cleaning action. Higher frequencies will also reduce the distance between damaged areas, since higher frequencies produce a more evenly distributed, less destructive scrubbing action.
In some cases, damage is not produced by the scrubbing action, but rather by vibrational resonance. Very thin glass, semi-conductor components, and other similar sensitive components are subject to this kind of damage. Items being ultra-sonically cleaned may fracture during the cleaning process. in these cases, parts should be test cleaned in various ultrasonic frequencies to determine which operational frequency can remove the contaminant in question, while simultaneously preventing damage to the component.
If items being cleaned already possess defects or cracks in the material, ultrasonic cleaning systems will tend to attack these areas aggressively. For example, ultrasonic cleaners are not recommended for cleaning emeralds, since these stones have natural veins in the material which are subject to vibrational separation. The same would apply to plates with cracks in them, or any other material with similar characteristics. In fact, ultrasonic cavitation will find leaks in tanks which do not leak when the ultrasonic system is not activated.