Let's say there is a patent for a gear covered in gasoline where the gasoline is explicitly mentioned to be used for the lubrication of the gear. Can I patent the same gear covered in gasoline embodiment where gasoline is explicitly used for cooling as it evaporates? Or let's say there is a patent of a gear covered in sugar which is explicitly for protection against hear. Can I patent the same gear covered in sugar where sugar is explicitly for protection against oxidation? Another example is, an antibody coated eye contact lens to prevent infection but also an antibody coated contact lens to lubricate the eye (supposedly that both functions of antibodies, i.e. infection prevention and lubrication are known).
No. First - you can't patent the same structure under a different theory of why you are doing it. Some claims (device, machine, system, apparatus, etc.) are to a thing. Your "new" thing is exactly the same, structurally as an old thing so this is 100% out.
In the other example, if your antibodies are different antibodies then you have a different thing and are potentially OK.
Second - Patents are also given for methods or processes. You could write a claim for a method of cooling a gear by immersing it in gasoline. It would be, in your hypothetical, rejected as not new in the U.S. becasue of inherency. The steps of the method have been performed before, just for a different reason.
If you could patent something old due to recognizing unknown inherent properties you could stop the making and using of something that pre-dated your application and that is taking something existing away from the public, a very big no no.
To get a patent, an invention needs to be new, useful and non-obvious. New means no one knows about it. Useful means the invention must work. Non-obvious means someone skilled in the art wouldn't find the invention readily apparent.
A snarky answer to your question is that because you have publicly disclosed your inventions they are known and not now patentable. However, in the US there is a grace period and I'm assuming these are just examples and not real inventions you want to patent.
One thing to remember is just because you might get a patent on something doesn't mean you have a right to use the invention. There might be another patent that covers the invention. I think this is the problem with several of your ideas. For example lets consider your gear using gasoline. You might attempt to get a patent on the use of gasoline to cool a gear. I'd say this would be obvious since evaporative cooling is well known and cooling a gear train is also well known. However, even if you did get a patent the original patent with covers a gear using gasoline to lubricate would be infringed. You might say "I'm using the gasoline to cool", but the gasoline doesn't magically lose its ability to lubricate. If you implement all the aspects of a patent's claim, you infringe it. Similarly if sugar prevents wear and oxidation, you might get a patent on the oxidation prevention, but the sugar doesn't lose its anti-wear properties so you are probably infringing on the existing patent.
Similarly using antibodies for infection control and lubrication. Assuming the antibodies actually have both properties, if you make contact lenses with antibodies and claim to use them for lubrication, they still prevent infection. However, you might work around the infringement if you devise a particular antibody that can be proven ineffective as an infection control but still has its lubrication properties.
This all boils down to patentability versus freedom to operate. I am not a lawyer and patentability and freedom to operate analyses are highly dependent on the particulars of the invention. I highly recommend working with a patent attorney or agent with experience in the specific field.