You cover with the band-aid only when medicating.

Not for every day use.

When you apply ANYTHING to the skin, and cover, it penetrates better. Saran wrap is used in some derm treatments for this reason.

To get penetration of an agent into the toenail, covering it enhances this.

You apply the agent, to a clean dry toenail, and if you cover it the medication will go into the area it needs to go. Some products have a "new skin" additive in them to cover the medication. This is a clear chemical that dries like nail polish.

But doing Vicks, one would have to cover, since there is no additive in that.

There is a distinct difference in HEALING, and prevention.
For example, it used to be in the old days, that you left a cut or sore open to "air out"... Not any more! Turns out that certain healing factors prefer moist situations.
http://hyamin.blogspot.com/2008/05/w...er-or-not.html

We see today many new treatments including some Band-Aids in drugstores today, designed to keep on wounds for 3 days or more. There are some used in nursing homes that stay on a week. They are made from a special material, and don't need changing so often. Regular bandaids would need changing at least once a day or more.

Dr. Paul's remedy needs covering to force the thymol into the growth plate of the nail, so new cells will be resistant to the fungus. That is how it works. (not by primarily killing the present fungus that is there, but driving it out.). Some drugs like griseofulvin work this way too...they take several weeks to work therefore. (and many of them are quite toxic long term).

The bottom line is to see a podiatrist to find out what is really going on and how best to deal with it.