The elaborate refrain too has a *very* modern ring, with its imperative (to no obvious person) to "swing around the merry-go-round." That combines with the "wheel of fortune" in a subtle suggestion of the runarounds and ups and downs of life and love - an allusive symbolic approach pretty typical of the singer-songwriters of the 1960s, and popularized by Bob Dylan.
MtheGM, I can't place the tune, which also sounds "recent" to me, but I'm not an expert.
Note: "recent" to the likes of us means "only forty to fifty years old." To a great many people, in other words, the song is "pretty damned old."