During the early part of the 1980's, the RI Historical Heritage & Preservation Commission did surveys of the antique & historically significant structures/sites in all 39 RI municipalities as well as some other surveys of specific neighborhoods and structures of a specific classification such as historic bridges.
The print versions have long ago gone out of print but each town's/city's survey book is in pdf form at the RIHHPC site.http://www.preservation.ri.gov/survey/publications.php
I believe the property you're interested in is refered to as the Hopkins-Tucker-Gairlock House in the book. The inventory is organized by road and your property is found on Tucker Hollow Road, deacription starting on pg 78.
All the description says about the builder is that is was "a Hopkins, possibly Joseph". The Hopkins family, being one of RI's oldest, has numerous members as well as Hopkins to Hopkins marriages to challenge the researcher.
One would have to trace the property back from the current land evidence books back through the older deed books to possibly determine just who originally owned this property around the time of the home's construction.
Try looking at Google Books for town histories & privately published genealogies to possibly pick-up hints and leads about the house. Internet Archives will also have books of this sort available.