It'll be tough not to have it reset after changing a page. You will HAVE to use frames, or, preferably IFRAMES. Your best bet would be to have one that shows it's content based on the time on the clients computer. I might try to make you one later.
EDIT: I can't make it due to lack of time. You'll have to make it yourself.

look since you want it not to change, you should use iframes. (I am assuming you can code. If not, post a code request in the Codes section). What you should do is create a new html document.  In that you add a code that will write to your page. Have it so the timer will depend on the time. Set a time-out so it refreshes the page at regular intervals. Then host that page somewhere and have an iframe pointing at it. (<iframe src="URL"></iframe>)

I don't think there is any. But I bet you could request one at SMC(look at my sig for the link).