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You can replace the bimetallic switcher (not constant voltage at all) with a cheap voltage regulator like a LM317. You would have to build the circuit although its only a few parts. The gauge system draws quite a bit of current.
Maybe you know this already, If measuring with a digital voltmeter it's going to look wonky. It's pretty choppy, since it's an averaging unit. It makes and breaks 12 volts a couple times a second mechanically, consequently "dropping" the average voltage the dash gauges see, they respond sluggish by design so everything works fine. They do go bad, but are often replaced unneccesarily. Try measuring with analog type meter, it's probably working fine.
It would be a lot easier to buy one, but if you have hobby electronics skills, you can make one easily. I used junk-box items. If you make your own, you can add a transient protector across the leads, use better caps, and a better heat-sink.