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ok, that bit is a pawl, see if you can find a fix related to that. honestly though, unless you can see an obvious problem, such as a spring having popped off, I would leave it.
they're complicated and fiddly to put back together. even if it was taken apart and you found a broken part I'm not sure you could get spares. it would be easier to just replace. give it a try but it will be tricky to get working again. its not one of those things with a certain fix at the end.
unfortunately if it was the lever not doing anything, there an easy fix for that.
Dogtemple-
Appreciate your input.
It seems like it "should" be a fairly simple fix. If I tip the shifter upside down, gravity pushes the pawl into place and I can shift through all the gears perfectly well. It seems like the pawl just needs some pressure on it keeping it in place and without seeing the internals of this section I can't figure out where the pressure should come from/why the existing set up isn't providing any.
Dropped.Bars
I mean the little ratchet. When in an upright position, as the shifter would sit on the bars, it drops down off the the teeth of the mechanism as there is no tension on it.