There are two elements to identification: production epoch and model.
The presence of the sink-style splash well and without notched transom for 15-inch shaft identifies this boat as being from the "Smirk" era, that is, c.1972 or newer. The shape of the bow locker suggests 1977 or newer. The seller's representation of a 1982 model seems appropriate.
The model is easily deduced from the seating seating arrangement, which appears to be mostly stock, indicative of the SPORT model. The original seats were fine mahogany planks; perhaps someone took white paint to them. Or perhaps they are replacements of unknown origin. Have you seen the REFERENCE section on 13-foot boats? Visit
http://continuouswave.com/whaler/reference/13/The bow railing looks a bit out of place. Perhaps it was added after initial purchase. In the 1980's Boston Whaler offered many options, so it is not beyond the realm of possibility that the tall bow railing was installed at the factory. A close visual inspection might reveal some details that could tend to confirm or refute that. But my feeling is that the bow railing is atypical and probably added later by someone who owned the boat or by a dealer. The tubing diameter looks out of proportion (too large) and the presence of rust stains at the bases is indicative of poor welding or not very good stainless steel; those are non-Boston-Whaler markers. A factory installed bow rail would probably look more like the one shown below:
Once you have the federal HIN or the Boston Whaler stencil number, you could ask Boston Whaler customer service if they have a record of the bow rail as an option on that boat. I am not 100-percent sure they track all old hulls with that level of detail.
The engine rigging on the boat is sloppy. That old Mercury could be a decent engine if it has been well-maintained, if the electrical modules for spark and battery charging are working, if the wiring and rubber hoses under the cowling are in good condition, and if the fuel lines and primer bulb don't need replacement. But the old Mercury could be a source of trouble and need attention of a good old-school-from-the-1960's mechanic if it doesn't look like it has been kept in tip-top shape. It should start easily and run smoothly, but with blue smoke aplenty in the exhaust.