Hear me through before you stomp on my joy. I clicked on the "Random Page" link on the Dwarf Fortress wiki and came across the "Mechanical logic" page. I saw that several of the logic gates required a Load (extra baggage to stop the gate when connected), and thought "there must be a better way to do this." I experimented a bit and came up with (in my book) a better way. Construct a lever, link it to a gear assembly, pull the lever, deconstruct the lever. Congratulations, the gear assembly is now inverted. While it does waste a mechanism, the extra stone/wood/mat required to make the load usually wastes more stone/wood/mat.
Before I started filming this video, I created two gear assemblies and a lever. I linked the lever to one of the gears, pulled it, and then linked it to the other. Voilą, they toggle.
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