I built a few clocks some years ago, both with the early DC106
modules
(tube and diode based) and the later DC111A/B modules (transistor and diode based). Burroughs even described how to build clocks in some of their datasheets where they showed how to eliminate some spade positions if you wanted to count to any other number than from 0 to 9 and a clock was one of their simple projects.
To get a scale of six counter you can connect four consecutive spades together just using one set of spade components and using them as the reset signal to the flip-flop driving the Trochotron, it will then reset when any of the combined spades are hit by the beam. Then you just need a simple tube coincidence circuit for the hours portion to reset the clock to 00:00:00 when it reaches 24:00:00 (you'll have to modify this for a 12 hour clock though). Burroughs also combined two spades in two groups making the DC111B count 0,1,2,5,8,9 so no extra reset signal was needed, the original one from spade 9 was used - this way the beam skipped positions 2 & 4 + 6 & 7, you just hooked up the Nixie like 0-0, 1-1, 2-2, 5-3, 8-4 & 9-5 (Spade-Nixie#).
/Martin