I feel ya!
I don't think there is certain "path" to move from Tech lead to Manager. If the opportunity shows up, jump on it. Or go find that opportunity where a company is ready to make you a manager. Or go tell your CIO/VP about your ideas to help products or teams, if you have any. Look for Tech Advisor/Mentor kind of roles where you can move away from project-by-project role and impact at Organization level.
I have seen managers who do ONLY "people" management - they ask repeated questions like "What is the ETA? Don't give me tech talk...tell me when you'll finish. Can you put all these features in one Java class? what will I do if you get hit by a bus?" and other stupid stuff.
That's where your skill-set comes into play. Find an opportunity where you can leverage your tech skills, understand what the team is doing and help them manage those technical risks. Follow commonsense people management ideas: Be nice and don't be a prick, share info, joke around, etc.
If you like to get few pointers about this, please read "Managing Humans" by Michael Lopp
http://www.managinghumans.com/ and his blog http://www.randsinrepose.com/