It's really a simple duplexing scheme. Half the segments have a common anode connection and the other half the other common anode connection. So from 12 pins you can get 24 independent segments. 3 digits for M, 10M and H = 21 segments, segment B and C for 10H = 2 segments, and last segment is for PM indicator. Each output pin is labelled with 2 abbreviations. For example: HUB = hour units segment B, MTC = minute tens segment C. You could connect up 24 LEDs and figure out which side of the centre-tap winding will activate which half.
The scheme is slightly modified for 24 hour display. In that case there are "segments" HTB, HTC, and HTADEG, so that it can display nothing, a 1 (B+C), or a 2 (B+ADEG). The PM "segment" is then not needed. Clever.
Your biggest problem will be getting a suitable display. You could make segments with chained LEDs but that's a lot of soldering.