The Google Ngram is interesting but strange. If you change the language to "British English" by and large, all you get is American writers and books.
I suspected that "fork" was, in fact, a deverbal noun from "to fork" and a synonym of "forking", and this is confirmed by:
- [ < the verb.] A forking, bifurcation, or division into branches; the point at which anything forks. Hence, each of the branches into which anything forks.
c. The point at which a river divides into two, or the point of junction of two rivers; a branch or tributary. Chiefly U.S.
1692 in Maryland Hist. Mag. (1906) 1 11 [It is therin described as] Being in the forks of Gunpowder River by the side of the said River.
1877 J. A. Allen Amer. Bisons 515 Great herds on the east fork of the Salmon River.
It will be noted that "fork and forks" are treated equally, although the fork is the point of forking and the forks are each of the new roads.
We then have
d. of a road.
1855 Washington Irving Chron. Wolfert's Roost 371 A fork in the road.
If you look at the example of "fork of the road" for the latter half of the 20th century to the present, the vast majority are historical references, religious writing and/or military, all of which tend to be relatively stable.
Whereas a fork of the road, would indicate the verbal noun, Here, "fork in" has become a deverbal noun - a common noun.
This is a reasonable transition for a verbal noun to make with increased use. (NB whereas references to "forks of a river" would remain reasonably constant because of its rarity, "fork(s) of/in a road" would increase with the rise of automobile traffic.)
The difficulty is that the graph, as far as it is accurate, shows a separation starting about 1925 coinciding with car travel but accelerating violently after 1985.
This seems to be simply popularisation:
A Fork in the Road (The Miracles song) - Wikipedia 1984
A fork in the road makes an ppearance in The Muppet Movie: https://muppet.fandom.com/wiki/Fork_in_the_Road
and at sometime before 1988, Yogi Berra (allegedly) uttered the immortal words "If you come to a fork in the road, take it!" https://quoteinvestigator.com/2013/07/25/fork-road/ Although this seems to be a reprise of a 1913 witticism, it must have helped publicise the construction.
In summary then the change is probably due to cars and the transition from verbal to deverbal noun followed by popularisation.