This is a very hot guess and you are on the right track, although it's not correct. It was neither JD nor a jail, but the person was very close to Jefferson Davis.
I should add that the place and circumstances have been mentioned on this forum, so I consider this a fair challenge...
Another good guess, Gene, but Roger got it, being certainly in the advantage of having visited the place. The photo was taken in 1936 from a different angle and presenting a different way of display than the one visitors get to see today. So I'm glad it worked out to "minimize" your advantage, Roger!
Thanks to everyone for all your smart thoughts and guesses! https://en.m.wikipedia.org/wiki/File:Jud...ty,_FL.jpg