The OED has the following general meaning of seaboard:
The line where land and sea meet, the coastline; the sea-shore or the land near the sea, esp. considered with reference to its extent or configuration.
The first citation of this seaboard is from 1788:
"The Gnats are almost as troublesome here, as the moschetoes in the low-lands of the sea-board."
The OED doesn't seem to draw this connection, but I imagine this meaning came about as an extension of another meaning for seaboard, which is:
With prepositions a, at, on, to seaboard, on or to the seaward side (of a ship, etc.). Obs.
If you connect that meaning with other sea terms like overboard, it would make sense that the seaward side of a ship would be called a seaboard. And then saying that the coastline is essentially the seaboard of a landmass is a small jump.
Nowadays, it seems like "Eastern Seaboard" has become an idiom or set name for a certain region, and we don't really use it in the general sense at all (although I don't know anyone in the fishing industry).
Best Answer
According to this Ngram,
the phrase first appeared in books in 1935, disappeared until 1949, and experienced an early spike in usage around 1951. A spike reaching a slightly lower peak occurred in 1967, followed by intermittent but generally up-trending popularity until reaching another high point in 1985. A slight drop-off then was followed by a sharp increase from the early 90s up to a historical high in 2000, the last year of Google's Ngram-available data.
It seems the first use noted was in The American Spectator, Volume 3, Issue 34:
Whether the phrase originated with the author of this piece is not evident.
This version of the same Ngram of the phrase “on the wrong side of history” with a "smoothing" of 50, shows the general trend over time from 1800 to 2000.