Performer sang/played backup on cover of his/her song

This was one of those things most DJs would mention back when the song was new. And I’m sure about the same time I read it in either Rolling Stone or Calendar or something announcing the song. But, you’re right. Strangely, I can’t find an explicit cite. I dug out the CD booklet for my Echo greatest hits compilation, which doesn’t have any information on additional musicians, but does call out Manzarek as the producer on that track. Manzarek’s website mentions “collaborating” with E&TB, but no details as to the nature of the collaboration.
Another hint is this concert review from 1987 that indicates Manzarek joined them on stage for “three Doors numbers”. Manzarek’sobituary in Rolling Stone mentions “playing” with E&TB.
Now I’m intrigued. Is this one of those “common knowledge” things that’s actually wrong? He is explicitly credited with playing on another song from the same time period, “Bedbugs & Ballyhoo”; maybe the two got conflated?

Neil Young sang backing vocals for Emmylou Harris on her version of his Wrecking Ball. That was the title track of her 1995 album. Well worth a listen.

“Someday We’ll Be Together” (1969) was the last hit of Diana Ross and the Supremes. Johnny Bristol had co-written and performed the original version eight years earlier. For the Supremes’ version, Bristol went into the recording studio to show Diana Ross how best to vocalize the song. He ended up ad-libbing a kind of call-and-response as she sang. An engineer accidentally recorded Bristol’s voice with Ross’s, and those in the control room liked it so much they left Bristol in the mix. He comes in toward the end of the song.

Richard Thompson plays guitar on Bonnie Raitt’s cover of his “Dimming of the Day”.

Lulu had a hit single in 1974 with The Man Who Sold The World, featuring Bowie himself for backing vocals.

Good lord, I would not have recognized her…

In 1999, Jimmy Page teamed up with the Black Crowes on a two-night performance of mostly Zep covers and a few old blues tunes which resulted in a double album “Live at the Greek”.

John Lennon sang backing vocals on Jimi Hendrix’s version of “Day Tripper”.

Not backup, but Steven Tyler and Joe Perry played/sang on Run DMC’s version of Walk This Way.

Cheech Marin did the vocals for Korn’s cover of Earache My Eye back in 1999.

Jimmy Page also played on the Puff Daddy cover of Kashmir

There is a recording of the Foo Fighters covering Ramble On & Rock and Roll on the Live at Wembley Stadium DVD. Page & John Paul Jones played with them.

Of course there was the awesome No Quarter Tour for Page & Plant, but that hardly counts.

Tangential sad fact: until I was well into my 30s, that was the only version of that song I knew.