Bobbie Gentry apparently hasn’t been seen in any public capacity since 1981.
That’s a good one. She was unusually talented and one would think her style would go over really well today and she herself would be in great demand. She’s only slightly older than Dolly Parton.
I just read this article about Jason Everman, a musician who managed to get kicked out of both Nirvana and Soundgarden before they became huge. He kicked around the music scene for awhile, then joined the Army and ended up in Special Forces. He completely avoided publicity, although he was occasionally recognized by hard-core rock fans. The reporter who wrote the article was a friend of his from the early days and tracked him down to the remote cabin he now lives in. He hasn’t disappeared completely, but pretty close to it.
Lisa Gerritsen, of My World and Welcome to It, and recurring character on The Mary Tyler Moore Show. There’s some evidence she worked in the computer industry.
Gerry Rafferty, of Stealer’s Wheel and solo albums. Wasn’t he missing for many years before turning up dead?
Not sure if she counts as famous enough, but Kitty Burke, a nightclub entertainer, walked onto the field and batted for the Cincinnati Reds in a game in 1935. The Reds wanted to commemorate the event in 1985, but they couldn’t figure out what ever happened to Kitty Burke.
Not missing, but reclusive is what I heard.
Apparently his alcoholism ruined his career and killed him in the end. 
For purposes of this thread, if a formerly big star now has a mundane, ordinary job, leads an ordinary middle-class family life, and no longer performs, that that person “vanished”?
Last I heard, disco chanteuse Anita Ward, who had a huge hit with “Ring My Bell” back in my college days, was a high school math teacher. Has she “vanished”? Well, as far as the public is concerned, I suppose. But she’s not JD Salinger, hiding from the world. It’s more that the world has stopped caring about her, except to the extent that periodically someone listening to an oldies radio stations wonders, “What ever happened to her?”
Many of us know that Peter Ostrum of ***Willy Wonka ***fame never made another movie, and is a country veterinarian somewhere. Does that count as “vanishing”? Well, no. He can be found. He’s probably in the phone book wherever he lives. He’s just totally out of the spotlight, and has been for 40 years.
In the hard rock/heavy metal world the guy for this thread is Vinnie Vincent, who played in Kiss for a couple years and then formed his own band, Vinnie Vincent Invasion, which made a couple albums before it kinda morphed into Slaughter without him. That might not sound like a whole lot, but Kiss fans on the internet are utterly fascinated with the guy to this day, yet his current whereabouts remain a mystery. Here’s a Rolling Stone article from last year about him.
How about Betty Page? She seemed to have vanished from the 60’s through the 80’s.
Someone will be along to explain in depth, but you might check out her Wikipedia page for some eye-openers.
Oops, she didn’t quite fit the OP’s criteria. If only I had posted this in 1989 ; )
After you’ve done this
you're left with no place to go but retirement, really.If he counts as a WWII celebrity of sorts, young Arthur MacArthur IV seems to have disappeared himself quite effectively over the past 50 years.
He did a “where are they now?” reunion show a while ago (probably when the Tim Burton film came out). Michael Bollner (Augustus Gloop) is a tax attorney in Munich. The girls actually attempted to have acting careers, with mixed success.
Rodriguez I would tell you how it all turns out, but that would be a spoiler…
Be careful what you wish for…