Looks like the pavilion name may be inaccurate. According to this the pavilion is either Sugar Beet, or Sego Lily. Both on the south-side of the park, though one is east, and the other west. Both have nearby parking.

There's a map at the above site with the pavilions highlighted, to get a better idea, if you are unfamiliar with the area.

edit: After hearing from hamnox, the pavilion is Sego Lily, roughly south-west side of the park.