I've never used "teak oll". It's just a few basic clear oil finishing things like Tung oil and turpentine. Anybody can mix oil with paint thinner, turpentine. kerosene ect w oil that sounds good. Truckers use automotive lube oil, used or not on their wood planked flatbed trucks. When I was told to do that (used oil) I thought it was nuts. I thought oil promoted rot in wood. It was kinda oily for a week or two but it did keep the wood from acting like a sponge getting very saturated w water. Of course it was out in the sun and rain always except at times when being loaded inside a building.
They say Linseed oil is fungus food. I haven't seen fungus eating but I suspect all oil w/o poisons in it are good fungus food. Wood preservatives are all poison but the laws nowdays dictate the poison be so benign that it's hardly worth the effort. But you can add anything you like that's compatible w what your using. Beware of anti-mould additives only for water based house paint.
I mixed my own oil for my teak in Alaska as no finish seemed to last very long at all. It was OK in the cold climate but I doubt you'd like it in Florida. Fishermen in Alaska coat their wood decks w pine tar or asphalt tar. Yes their decks are sticky now and then but even protected from the sunlight. Go for it if you like black sticky decks.
Most commercial teak oils are basically very non-glossy, slow drying varnish. Varnish is oil mixed w a vehicle like turpentine or paint thinner. The additive package is much more important than w engine lube oils. I used raw Linseed oil and turpentine basically but varied the proportions of oil and turp to suit my need at the moment. Bare and dry wood l'd use 10% oil and 90% kerosene or turp. First coat or two I'd use kerosene instead of turp as it's best for penetration. See the book "Skiffs and Schooners" by R D Culler who is considered by many deep into the wood boat culture to be the god of all things wood and boat. He recomends putting as much kerosene in the bilges and practically everywhere else as it "drives the finish into the wood". The finish being whatever he puts in the karosene. So for at least the first coat or two I'd use kerosene instead of turp. Then basically I'd reduce the amount of turp and increase the amount of oil for successive coats. Having control over the content of each coat is a great advantage for oiling.
I used raw linseed oil but for later coats one should probably use boiled linseed oil. It dries much more or to a greater extent. One wouldn't want to sit on my caprails for a few days or a week after a late coat of oil. Too sticky. In dusty places dust may stick to the oil and perhaps ruin the finish but I had no trouble w that in Alaska .. SE Alaska. Soon or not long after the last coat of oil one could sit on my caprail and not pick up anything on one's clothes at all. It just feels a bit sticky but then I always used raw linseed oil. May not even feel sticky using boiled oil.
After several coats (or many depending on the percentage of oil ect) you will get to a point where you're happy w the finish. I tried to stop coating when I noticed some small spots halving a gloss .. looking a bit like varnish. Actually if you did want varnish what I've described so far is the best base for varnish that I know of.
The "teak oil" that I hear the most praise about is "Dayly's Teak oil" but you may not find it on the east coast .. it's a Seattle product. But it may be available everywhere in the US and perhaps beyond. I don't like it as it was too prone to build and become varnish. Didn't last as long as Linseed oil either .. on my application.
I put other things in my home brew teak oil but can't remember what they were. One could use Japan Drier, uv inhibitors if found, anti-mould and/or other poisons, stain or substitute Tung oil for the Linseed oil. Many think it's supperior. One could experiment w pine tar.
North Western Washington State USA