SP4: HTMLContainerCache and Chat turn off or on: header not flushed

No page is in HTML container cache. I turn on the chat (so it is activated and not grey any more). I put a few page in the cache. Then I turn the chat off. Go back on your previous pages. The chat looks like to be turned on again. Turn it on again and go on the page you put in cache when it was off. It looks like being off again. Quite rapidly this becomes a mess to know if your chat is turned on or off.

We should flush the user header (or skeleton) when the cache is turned on or off. Or if the header is a shared fragment and the impact on performance would be too high, this should be a dynamic AJAX call to the chat and not something which is cached in HTML within the fragment or the skeleton.