I myself come from a less than traditional path to PMM after spending the first half of my career on the brand side of the house. I may be biased, but I think less than traditional backgrounds are really valuable in a PMM and I typically look for a couple of key characteristics:
Trust Building
I look at roles this person has had before and ask about the stakeholders they've had to work with. So much of PMM is being at the center of a wheel where you need to operate without top-down automony. I look for stories of times where they were able to use the trust they built to execute beyond the normal scope of their day-to-day. This is an indicator that they've not only built trust, but that they knew what to do next when they built it.
Work with Technical Stakeholders
This may vary from company to company, but I've always worked in environments with a strong cultural of engineering and product leadership. I look for experiences that people have had dealing with technical stakeholders, be they engineers, PMs, analytics.
Insights
I look for demonstrated experience gathering insights from customers and putting those to good use. Many people have experience with the former, but often don't have examples of the latter where they were able to take those insights and make something of it. Whether it's crafting a sales pitch, a thoughtful advertising brief, or showing the impact of a more highly targeted growth campaign these experiences show that this person knows how to look for the truth and knows what to do when they find it.
High Empathy
Above all, I think a core of PMM is empathy. You represent the needs of customers and are expected to operate with soft power to get things done. Experiences where you've shown that you can do this and the referrals from partners who have been outside of the marketing organization carry significant weight in my book.