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I can't quite remember when I discovered the Robert Palmer version. At first, I thought it was Palmer covering Stewart, but later I learned that Palmer's version came out in 1982 on "Maybe It's Live". It still has an early 80's sound, and there's actually a video for this version, but it is 1) bizarre and 2) NSFW. I'm not sure why in 1982 you would make a video that you know can't play on MTV. Furthermore, he really only borrows part of the chorus from the original -- it is almost more of a remix than a cover.
After doing a little poking around on the Web, I learned SGHATL is actually a 1969 single from the R&B group The Persuaders. It was a top 40 hit for them then, but I don't recall ever hearing it on an oldies channel. Knowing that Robert Palmer based a lot of his material on R&B covers (and to a lesser extent, Rod Stewart as well), this made sense. And their version is quite good, even if it sounds modish as well.
A little more poking around on the web and I found that Derrick Harriot release a reggae / proto-dance hall version in 1974; this version is quite good too. Maxi Priest released another reggae version in 1987, but this one doesn't do much for me.
Saving the best for last, I uncovered on YouTube a "live in the tour bus" recording by Camera Obscura (whom you may recall from my glowing review of "Let's Get Out of This Country") which is, as far as I know, not available on any of their official releases. No disrespect intended to original writer Jeff Fortgang, or Robert Palmer, but Tracyanne Campbell is always going to trump the others in my book.
The Persuaders: YouTube.
Derrick Harriot: YouTube.
Robert Palmer: Dailymotion, TOTP version.
Rod Stewart: Dailymotion.
Maxi Priest: YouTube.
Camera Obscura: YouTube.