The "Quickstart for Using the Proxy for Local Testing" page sent me to the "Enable an API" page for the "Cloud SQL Admin API."
When I went there, and selected the appropriate project, it just sat there, with a dark gray "enabling API" message box.
Some weeks ago, when I needed another API enabled (something about deployment, so that I could deploy the Tomcat preinstalled instance), the page to enable that one explicitly told me that my account wasn't authorized to enable that API, and so I referred the API enablement to somebody who did have adequate authority.
This one gave no message that I didn't have adequate authority; it simply took my selection of project, immediately threw up the "enabling API" message, and then just sat there.
Any insights into what went wrong?