Context: Was product guy at Google (built a few cloud products, did some work in the open source ecosystem), now CEO of a startup.

Background: I don't think I picked product management, it sort of picked me. When I was a really junior engineer I worked in a small team environment with much more senior engineers. We didn't have product management support, so someone needed to talk to the customer and figure out what they needed, and then later have the hard conversation when we were slipping our date. That ended up being me. Someone needed to document what we were doing, that was me. At the end of the day when we had little management support, someone had to represent the needs of the team and hold the team together during an aggressive corporate downsizing. The team looked to me to do that. I sort of drifted into this role without ever being asked to do it. I loved coding, but turns out I liked solving business problems just as much. My path to proper product management went through program management at Microsoft which was a bit of a half-way house. Good customer passion but more focused on execution than on the health of the business.

This doesn't directly answer your question, but I hope is helpful: what are the attributes I have seen of successful PMs?
* Have good technical instincts. You don't necessarily have to code well but you need to smell credible to engineers and not have them flip the bozo bit on you. I watched a product guy argue that we should figure out how to reduce latency between global data centers and then someone kindly point out that speed of light was the problem at hand, and we really couldn't do much about it. Don't be that guy, you will never come back from that point.
* Champion the customer. Product managers have to really 'get' their product deeply, understand it, use it, live with it. They need to be able to see it they way a customer sees it and represent the hiezen-customer to the team. The primary work product of the PM is the PRD (product requirements document) and the customer should shine through.
* Own your business. It isn't enough to build neat technology, that people love, but if no one knows about it or you can't sell it you are wasting your time. Know your sales people, know your marketing strategy, understand the pricing model. Make sure they all get what the product does and is good for.
* Be the janitor before you try to be the CEO. There are a million things a team needs to do. The product manager needs to fill the gaps. Win by doing the things the engineers can't or don't want to do, but don't 'wall paper' over problems with the team structure. Remember however that doing a gap job well indefinitely gets in the way of creating high functioning teams. You need to work your way out of a gap filling job.
* Knowledge is currency. To lead, you have to have something and see something the engineers don't. Understand your competition, use their products, speak to a lot of customers, bring that knowledge back to the team and they will start to trust you.
* Stay out of execution: you are not a project manager. The eng function should not be babies, they need to hire their own project managers to run their scrums, organize execution, etc. If things go well for your product you are going to be talking to customers, negotiating partnerships, etc just as the team starts to hit an inflection curve in execution, you can't afford to be trapped in the office running their processes.

Hope that helps.