Are there many employment opportunities in the village of Red Hook?

I would not imagine so. Red Hook isn't a huge town and it seems more residential than commercial, but you can definitely find certain positions here. A search I did for jobs in the whole town of Red Hook (not just the village, the whole town) only turned up a couple dozen openings. The village has to have less one would think.

The sorts of positions you would find, if anything, would likely have to do with locally-owned businesses, or schools. I'm not a Red Hook resident so I can't say this for certain but the two closest towns with a more substantial number of jobs are Kingston and Poughkeepsie, so I'd assume a fair number of Red Hook residents work in either one of those.