You haven't stated under what circumstances more than one segment can light up.

The way to get this job done is to make a complete wiring diagram, at least of the display and the circuitry between it and the "clock chip", and subsequently make up a truth table, in which you show which segments light for each combination of inputs. That will also provide the signal combinations you need for each segment, digit, etc, which you'll ultimately need in order to do this job anyway.

RE