My guess is that this is the original spring located on the Fountain of Youth property which has since been plugged up. When the owner of the property unearthed a cross made of rocks in the ground with a nearby silver vessel holding a note from Ponce de Leon inside, the location of the fountain was moved there and they dug a well from which to produce water.
I'm not sure where this Sunken Garden postcard was based on; there was nothing resembling it on my recent trip to St. Pete's Sunken Garden. I love the text on the back, it reads:
"Florida is a delightfully sunny place, fashioned by nature in her happiest mood, endowed with super fine gifts of climate, beauty and salt-ladened health-giving winds and smiling skies."