My shower diverter leaks whenever I turn on the taps. I have an old faucet (pull type diverter ) that is located between the cold and hot faucet.
Once the flow on the hot or cold tap is strong enough, I can pull the diverter and the leak from the diverter stops. I unscrewed the cover off diverter and the unscrewed the brass nut that covers the pull rod. Once I get to this point, how do I remove the pull rod to find the source of the leak?

What brand? Is it a delta? Moen? Long or short diverter?

I don't know. How do I find out? The diverter is a long one.

Look here and find your handle... Kissler & Co., Inc. (http://www.kissler.com/)