One of the things I appreciate with people I work with are that they are engaged, and a good product owner is no exception to this. Thus, in the list of four characteristics of a good product owner, I would like to start with that one.
With "engaged" I basically mean that the product owner should care about the product that we are working on together. This manifests itself as the product owner wanting to participate.
For example, there might be a problem with some story that is under development - border cases might be unclear or we have unveiled an alternative flows that we did not foresee. In that case, the product owner should consider it important to discuss those to help the development move forward without stopping. Or, if there is a business concept a developer do not understand, the product owner should want to explain it.
Further than that, the product owner is not just reactive. The engagement is also proactive. As an example, there might be a story on the backlog that the development team has deemed too big or unclear to start developing. The product owner should then consider that important enough to work with stakeholders and developers to re-phrase that story in a way that makes it more feasible for development, e g by delimiting it or splitting it.
Being engaged rules out product owners that became product owner "because someone had to be" or - even worse - where ordered to take that position, perhaps against their wish. Such a person will have no particular interest in the system, how it is used, or how it should evolve.
So being engaged is mostly about informal situations - like being involved - not about formal decisions. And it is also an attribute in a personal context - like being decisive - not about what the surrounding organisation lets you.
Having an engaged product owner is crucial for sustained success in development.