I've been through the process of finding non-technical co-founders, growing companies, and raising money. Along the way, there have been a lot of lessons learned about non-technical co-founders.
First, remember that as a technical co-founder, you will likely be the CTO/lead engineer. Your non-tech founder will probably be the CEO. The CEO has to manage early customers, investors, and partners. Most of their time is spent communicating the vision to these people, and hence they naturally end up directing the vision more.
On the flip side, you will spend a lot more time heads down coding. This relationship often makes it feel like you are "working" for the CEO, and you kind of are. Such is the nature of CEO/CTO dynamics, and I think this is why a lot of technical people resent non-technical co-founders. So ask yourself, are you comfortable working for this person who will probably be your CEO?
As a corollary to the previous question, have they managed or worked with engineers before? Have they ever been in a technical role? If not, you will run into typical Maker vs Manager problems. It's hard to work with non-technical co-founders who don't understand the mindset of technical founders.
As mentioned, watch out for consultant/banking types who have no real experience running companies or in startups.
Also watch out for people who are divorced from the product/passion and don't really get the pain point. This is the guy who has a friend who has a buddy who made money in a startup, and now he wants to do one. All they see is dollar signs. They might as well be pushing another hedge fund, "strategic partnership", or snake oil. They don't really care, and they suck the life out of startup.
My favorite non-technical co-founders are people who were engineers in a previous life, but have since found their strengths in product or customer development. They are well connected from having worked in startups before (which probably means access to talent) and possibly have an MBA (which often produces connections to funding).