Are you sure it is "Brooks" and not "Burns"?

Burns Court still exists. It is a historic section in downtown Sarasota, probably best known hereabouts for an artsey motion picture theatre, the Burns Court Cinema.

The West Coast of Florida was loaded with Army Air Corps bases during WWII. They were usually known as "fields", as in Tampa's Henderson Field, Drew Field and McDill Field. I don't know what is today Sarasota-Bradenton Airport (SRQ) was called then, but you can check out the airport web page.

The Sarasota Herald Tribune newspaper archive yields over 1000 hits for Burn's Court. Check out the results for a web search: "Burns Court in Sarasota".

If I can be of additional assistance email hgordon@wcts-sarasota.com.