We need to confirm which wires are pairs for each coil. The original diagram you posted has them listed as Green & Red as one pair and White & Black (plus shield/bare) as the other, so we need to check that's correct.
Disconnect the Hot Stack's wires from the mini-switch, set your multimeter to 'resistance' (Ohms) and test the green/red pair and white/black pair. You should get a resistance reading, probably 4K+. If you don't get a reading then start switching the pairs, red/black, white/green etc until you get measurable resistance and those are your coil pairs (this video may help).
Also test your mini-switch to ensure that's working correctly. Set the multimeter to continuity test (or resistance will do) and test the switch contacts in each position. Remember, as Simon posted, there are type different 'handed' versions of the on/on/on's so you'll need to test which version you have (as per Simon's image, types 1 and 2):
The testing will tell us what's working or should be working and how in needs to be connected. Make sense?
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