To answer your last question first, you start looking for the summer before you graduate. In your case, that would be June-August 2016. The NHSC usually has a retreat or a webinar, where they explain how you interview for jobs, what your requirements are, and what benefits the NHSC offers (moving stipend, etc.) They usually include an updated list of available sites.
There may be many reasons why you never see any jobs listed for the region that you are interested in. The region's HPSA score may not be high enough for a Scholar. There may not be any openings. The clinics there may not need anyone in your specialty. Etc.
If there are approved clinic sites in the general area that you are interested in, it does not hurt to email their HR representative and ask some questions or express your interest. The one thing to remember about almost all NHSC sites is that change is a constant. Theit providers leave. They decide to open a new clinic site, or expand a clinic. They get a new grant to offer more services. Things are always changing.