The production month coded as "S" does not work. Let me try again.
Note that I posted an earlier response rather early in the morning before coffee.
Upon further review, I note for 13-foot hulls the HIN production sequence number coding begins with a sequence of A1000 to A3999, then jump to B1000 to B3999, and continues in this pattern. This would allow the production sequence number to rise to M1000 to M3999. Your production sequence number is M1036 fits this pattern.
The basis for assumption that the sequence proceeds upwards to at least M1000 and beyond can be inferred from the comment that the sequence allows for unique identifiers for 54,000 13-foot hulls. Each letter prefix increment provides for 3,000-hulls to be identified. If you divide 54,000 by 3,000 you get 18. Counting letters in the alphabet, but omitting the letters "O" and "I" and "Q" to avoid confusion with zero, one, and zero, the sequence is implied to reach to at least U1000 to U3999. On that basis a production sequence number as M1036 would certainly be possible. The basis for this analysis is a drawing from Boston Whaler dated 1992, which is linked in the FAQ answer I mention above.
The new analysis of the HIN you were given as belonging to your 13-foot hull is now as follows:
BWC = the manufacturer identity code (MIC) for Boston Whaler;
M1036 = the five character production sequence identifier, indicative of a 13-foot hull.
5 or S = both "5" and "S" are not allowed as encodings of the month of production. I will speculate on what this character might have been, since we do not have any visual image of the HIN, and we are relying on something some unknown person wrote down some time in the past history of this boat.
In order for this HIN to be for a Boston Whaler 13-foot hull as a 1988 model but be build in 1987, the month of production would have to be in the range of JULY to DECEMBER, which are encoded as follows:
F = June
G = July
H = August
I = September
J = October
K = November
L = December
Looking at those possible letter characters, it seems like G could be confused for a "6". Perhaps someone wrote down "6" instead of "G" when they were transcribing the characters in the HIN. This also makes good sense because the earliest month a boat could be built as a 1988-model in the preceding year 1997 would be in July 1997. The other month codes, H-I-J-K-L, do not lend themselves for confusion, although perhaps an "I" could be read for a "one." But this field is REQUIRED to be alphabet characters, so anyone who was familiar with the HIN format would never record a numeral in this field.
7 = a single digit indicating year of manufacture, in this case 1987;
88 = the model year designation, in this case 1988.
As I explain above, I now think the HIN for your boat is actually
BWC M1036 [one of the letters G-H-I-J-K-L] 7 88
An embossed molded-in identification should be somewhere on the boat, unless for some reason the hull was damaged and was restored with new gel coat layers, and the original HIN was lost in the process, perhaps sanded off in the refinishing process or sprayed over enough to conceal the embossed characters which typically would make indentations in the hull.