What is the qualities of a Product Manager that impresses their Engineering counterparts and thereby allows the PM to build influence with the Eng team?

Being a team player and sharing team responsibilities e.g. sharing scrum ceremonies with your EM, will help you be equal partners. 

Don't forget that while you're doing customer calls, aligning stakeholders, or writing PRDs, your EM is directly managing the engineering team. This takes energy and time. 

I get the gist of the question, yet want to call out that "impressing" team mates is not the path I would take. Rather its all about how one can show up authentically and build a collaborative working relationship. It also set ups a paradigm where one party gets to define what is valued and the other just has to respond / adapt.

So I would recommend something like this (note: this applies not just to your engineering partners but also everyone in your Trio+ sphere). Essentially I want to consistently demonstrate three things.

I'm real...

• I do what I say and keep my commitments.

• I'm going to act the same whether its just us, in a big group, or with our bosses.

• I'm going to make mistakes and have to apologize for stuff

I'm safe...

• I wont throw your or the team under the bus

• I wont grab all the credit / not acknowledge our team efforts

• Mistakes happen, lets face it as a team

I care...

• I will be present for and engaged with the team

• I will own my responsibilities as a PM

• I will get to the right level of technical knowledge that fits the needs of our work

• My Trio partners are equals

When all three of these factors are healthy, we are going to be in the high trust / high collaboration zone and mutually influencing each other to achieve great outcomes.

A great Product Manager is being a good partner with the Engineering team, as well as the rest of the cross functional team. A good partnership means inputs from the entire cross functional team are valued and encouraged. Including engineers early in roadmap plans or design studio sessions increases collaboration and engineers should bring in Product Managers to weigh in on different levels of implementation and tradeoffs.

A CEO once told me that he would only hire a person if he thought that he would enjoy the time spent with that person despite being stuck at an airport with them waiting to board an indefinitely delayed flight. Despite the exaggeration, I've always imagined the equivalent scenario as whether engineers would want to spend hours with a PM in a war room or a bug bash.

Be an engaged partner. Be in the trenches with them. Work hard or harder. Follow-up and follow-through on your stuff. Be transparent about the real business context, the one they may not have heard. Tell them about what you are up against. Bounce ideas off of them, ask about options, be curious. Be their ally, advocate, or sounding board when needed but not blindly. Don't just toss a problem over the wall. Write a technical PRD vs a one-pager. If they are "not delivering" don't just report it as late in a status meeting. Meet proactively- ask what can you do to help them do their part. There could be a zillion other reasons- they are working on something else that's more important, or even less important but they didn't know otherwise, they don't know how to "fix it" yet, or they are dealing with personal issues, etc. Admit your mistakes and help them recover from any of theirs. This does not mean sweeping real issues under the rug. Address things that cause real damage head on privately or less privately as needed.

By now you may have noticed that none of my answer contains anything about having more technical knowledge. It is also true that getting increasingly more technical will always help. But it won't impress or influence. Being real and human is more impressive these days; it will build trust, and trust paves the path to true influence, one that cannot be confused with coming from title or power.