Open a new browser window just for that tab. Presto, that tab is always active, even if that window is underneath another window.

In Firefox you can drag'n'drop a tab "out" of the tab bar, which will move it to a new window. Might work in other browsers too.

Unfortunately, browsers "solved" this by intentionally adding APIs that enable websites to do this to you. It wasn't possible to abuse users this way until the relevant APIs for detecting focus and occlusion were added. :(