A friend gave me a cutting in the hopes that I could get it identified here.
I've attached three photos of the cutting, showing a close up of a leaf, a closeup of a berry and the third shows the configuration of the branches, berries and leaves. The leaf is 3/4" long, 3/8" wide.
With respect to your name and posted location, I'd suggest this is yaupon holly or more specifically Ilex vomitoria. Tons of it around St Augustine. I lived there.
The latin name means what you think it sounds like, but it's a lovely small tree, and sometimes a too common pruned shrub. Go to any bank and you'll probably see some grown as green hedges. The unfortunate name is referencing the use of Ilex vomitoria in the Black Drink as an emetic. Heavily brewed in tea, the tannins in the leaves will make you hurl.