You said you are drawing over the html page -- that implies that you are specifically concerned about seeing the html page under the plugin. If you use the plugin to draw, that means you have to use a windowless plugin -- windowed plugins cannot have transparent backgrounds. I'm not actually certain that all windowless plugins can even have transparent backgrounds, in fact.
Keep in mind that if the plugin is drawing over the page, that means the element is floating over the page as well -- which means you can't interact with the page. You'll basically need to handle the RefreshEvent and get the hDC from the PluginWindow and then draw using that, but as I said I don't know if it will actually work or be consistent or not.
If I were you I'd try to find a way to draw using html -- floating transparent images, for example -- and just use the plugin to do the eye tracking stuff.