I found several references online to the joke in relation to the song title, and that seems to be the most supported by the evidence. I can’t really find any support for the idea of sexual overtones.
Yep - I recall Plant being interviewed and saying “we were just trying to do a reggae song” IIRC, the title has nothing to do with the lyrics, they just were going for the name Jamaica - as in birthplace of reggae - and the old joke mentioned above. He talked about how silly it was to hear Americans come up to him and ask him about the song “DYE-ur MAKE-ur.”
And remember, white though they may be, LZ loved a number of genres thought of as being African, African American, etc…JP Jones was interviewed (VH-1 Legends?) where he talked about Bonzo’s love of Motown and Soul and that was why Kashmir big, plodding drum beating moves so nicely - he spices up the beat with Motown-style cymbol work. And let’s not forget the Crunge, which is meant to be James Brown, complete with “Take me to the bridge” an homage to Brown’s always asking his sax player, Maceo Parker to take him to the bridge ("Maceo - Maceo!!! you ready to take me to the bridge?! Take me to the bridge - hey-ey!!!)
Not to mention the black origins of the blues. Nope, LZ maybe some British White Boys, but they got into the roots of it…
Well, I was kidding obviously. I think it’s funny that a band excelled in one foreign style, the blues, couldn’t make a reggae song that sounds, to me anyway, anything remotely like reggae, while other UK bands (The Clash, for ex.) had no problem with that.