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Is that a double sided circuit board? If so, make sure you solder it on the top and the bottom. It looks a little black in the picture, so make sure you scrap it off a little bit with a knife so the solder will stick.
i have no idea if its double sided or not. I did find it strange how soldering that one wire back in did absolutely nothing, so maybe it isnt getting a good connection?
It's hard for me to tell from the pictures, but see the little lines that go from solder joint to solder joint? Are these little lines only on one side or are they on both sides? If they are on both sides, it's a double sided circuit board.
If the worst case scenario occurs a guaranteed used cluster could probably be had from eBay rather affordably for the most part.
Those PMOS boards would almost certainly be double-sided, the component density suggests that.
Without a working knowledge of that specific board and circuitry the average electronics shop won't be much help.
Not good news I know but having dug into a few of the older style analog odometer clusters a schematic or deep working knowledge is about the only way to effect most repairs such as the OP is experiencing.