Strunk illustrates with two examples—one with and and one with but—before continuing with the following prescript.
"Two-part sentences of which the second member is introduced by as (in the sense of because), for, or, nor, and while (in the sense of and at the same time) likewise require a comma before the conjunction."In other words, Strunk, while largely agreeing with the spirit of FANBOYS, differs in the details. Firstly, where we currently have FANBOYS, he had FANBOWA. (For Strunk, so was an adverb requiring a semicolon; yet is not mentioned.)
Secondly, nowhere does Strunk write, "coordinating conjunction". Instead he distinguishes between conjunctions that join independent clauses, and other conjunctions that “likewise require a comma”. This suggests that he thought for, nor, or, while, and as introduced a dependent clause, though I can’t think why or and nor are listed here.
So The Elements of Style (Geoff Pullum has called it, a "vile little assemblage of stupid advice about usage") is a little confused about or and nor, but doesn't seem to be the source I was looking for. This clue does suggest, however, that FANBOYS has its origin sometimes after 1935, when TEOS came out.
BTW, Schoolhouse Rock had it right: and, but, or & nor.