In the meantime, here's what I'd call a true pocket park. As far as I know, it doesn't have a name. It's a wide spot in Montecito Street (actually, the street splits in two and runs around both sides of the park) between Longfellow and Irving Avenues — in the Poets’ Square (also often called Poets’ Corner) neighborhood just east of Randolph Park.
The park has benches around a mesquite tree, with a drinking fountain for parched bicycle riders (and others :). The benches have mosaic murals — which you can see on today's entry in the Tucson Murals Project blog.
Location: North of the home at 4050 E. Montecito (click on the Location link below for a map).
Hours: Nothing posted, but 8 AM to sunset seems courteous to me. (There's not much light at night, and neighbors need their rest...)