I had to find out why Jeanette was just standing there, and this article explains it:
While Barbara and Eleanor skated, dipped and weaved to the rhythm, Jeanette stood stock still to their left, looking detached and aloof, holding her microphone down by her waist. When she did finally raise it to her mouth, she purposefully lip-synched the words rather than sing them.
Everyone assumed it was just part of their shtick. "Yeah, that was her gimmick," agrees Rodney Bingenheimer. Barbara recalls Greene and Stone also saying, "Yeah, it's different. Keep it!"
But Chelsea thinks there was another reason. "Everybody said, 'Why does she just stand there?' Most of the time Greene and Stone would have her mic turned off because she couldn't sing R&B. She felt left out. I didn't notice that was happening because I was overpowered by Charlie Greene."
Jeanette Jacobs, member of The Cake, close friend and lover of Jimi Hendrix, and wife of Chris Wood of Traffic has all but disappeared from rock history. Finding anything on her online that isn't incidental information from when she dated Hendrix or was married to Wood is almost impossible.
She had epilepsy -- one article online speculates that her "out of it" look in the performance is a result of her epilepsy medications -- and she died of a seizure at a young age. The date of death is listed 1980, 1981, and 1982 in various articles across the web, but this site about Chris Wood says she passed on January 1, 1982. Wood passed away in 1983.
That is a great article about The Cake at the first article linked, by the way. Highly recommended, although it is hard to read because the formatting screws up quotation marks in my browser, though.