There is a great half-hour tape labeled as Garcia-Saunders at the Matrix, May 11, 1971. I had always thought it was a little suspect, as I had never seen any other corroborating information, though it is listed at the Chicken's Matrix List.
This calendar listing from the San Francisco Chronicle (May 10, 1971, p. 45) not only puts JGMS at Matrix on Tuesday, May 11, but also Wednesday, May 12 - a new show to The List.
For color, I have been entering most everything I come across for 660 Great Highway. In 1971, I track Keystone Korner listings, since Freddie was still running it. I have also been entering the Tuesday auditions at Fillmore West whenever I find them - they have historically been absent from the Chicken's Fillmore West List, which originated in posters (of which there were none for the auditions).
No, I don't know who titular Jack is. I assume it's related to the SF mayoral elections, as many benefits seem to have been held at Friends and Relations. I assume based on today's electoral calendars that these were primaries, to select party candidates for the ca. November elections, but I don't know that.