The square slave dial that came with the later 1976 clock has an extra contact set attached that gives a pulse every 30 minutes. This is achieved by having two pins on the 'count' wheel, positioned at 30 minutes and 60 minutes (circled red), that lift the contact set as they pass by. The 30 minute contact set being the one attached to the diagonal bar running across the unit.
Because the wheel moves around in 30 second intervals the pin that lifts the relay springs would normally keep them raised for a full 30 seconds, until it is stepped on again by the next pulse.
To overcome this problem there is an additional contact (top right circled blue) attached to the top of the impulse arm. This contact makes briefly every time the magnet operates, but it is also in series with the contact set mentioned above. The result is that if the 30 minute springs are closed and also the armature is operated, you will get a short output pulse. The impulse arm contact set (blue) serving no other purpose during the intervening 29 minute 59 second periods.