Hendryx was quick to join the Black Rock Coalition, a nonprofit founded to counter racism in the industry, and raised money for H.I.V./AIDS and L.G.B.T. causes. Publicly out early — “It’s an open book,” she told The Advocate in 2001, of her sexuality — she has been in a relationship with Vicki Wickham, a British producer and Labelle’s manager, since 1971. They’ve lived in a rent-stabilized Upper West Side apartment, with one room as Hendryx’s gear-filled studio, for more than 40 years.

“She’s been very comfortable in her own skin,” said the tennis star Billie Jean King, a friend for about that long. “She doesn’t go, ‘Oh, well, is this good for my image?’ She’s very authentic. It comes from the center of her being.”

Hendryx releases music only sporadically. “I really, truly know that fame is fleeting,” she said. “And actually, money is fleeting, right? So my joy is in the doing.”

And her doing is often wildly imaginative, like the multi-sensory homage to Sun Ra that she organized at the Met Museum’s Temple of Dendur on Leap Day in 2020.

Clinton, the 82-year-old Parliament-Funkadelic frontman, is her longtime brethren: He did her hair in the ’60s, when he was still a New Jersey barber. A few years ago, after a show, they danced on tables in Ibiza. “A lot of musicians our age are not relevant at this stage in our life, but she’s been able to stay in touch,” he said, because she was experimenting from the jump. “You do that with a risk of not being normal or top of the pop charts,” he added, in a phone interview between tour stops. “But you last much longer.”

At the Betty Davis tribute, in a white blouse with twirling, floor-length sleeves, a skintight holographic silver suit, pompadoured ponytail and big-eyed butterfly glasses, Hendryx looked like she beamed in from a planet only inhabited by Prince (whom she also collaborated with). She frequently ceded the spotlight to her background vocalists, but when she came forward, she killed: Bringing out a falsetto and a growl, she performed almost an entire song in a deep crouch at the foot of the stage, then twerked from atop the drums.