I live in a Vermont town of about 600 people, and according to the 2022 town report, we have three Fence Viewers, along with a Weigher of Coal/Measurer of Wood.
For the record, I have no idea what the weigher of coal would do if I showed up to his place and asked him to weigh a load of coal for me.
My favorite is the Measurer of Wood and Bark. We elect one every year still as a lark, but it used to be important as wood was the central way people generated energy in their homes so standardizing wood lots was of central importance in New England.
Party affiliation for the Fence Viewer is not listed on our town's report. At least here, it's an appointed position. I have no idea if this is true everywhere though.
I haven't lived here long enough to know if the Fence Viewer being called upon to resolve some dispute.
https://en.wikipedia.org/wiki/Fence_viewer