The startup has not been incorporated yet. It has 2 non technical- and non business-oriented co founders who thought of the original idea. They got government non-diluting grant of $50k, and they used it to develop a technological POC (paid to developrs), and submit a provisional documentation for a patent. They are looking for a CEO and a CTO to take it to the next stage (seed round, and getting to product-market fit). They will continue contributing to the company, but have no distinct role in its next phase. I have an experience of beening the the co founder and the CEO of a funded company.
Some questions you'll want to answer before moving ahead:
How strongly do you believe this idea can become a successful product?
Why do you think they approached you?
How comfortable do you feel running a company owned by someone else?
What happened in your previous CEO role?
What confidence level do you have in the founders?
I personally wouldn't take on such a role, because there's no way I would ever run a company I didn't own. Too much blood, sweat and tears need to be put in for the return of a salaried payoff. I know you're asking about equity but are they even open to giving you some? Around 20% is the minimum, one-third feels right. They're never going to give you more unless they are crazy or totally inexperienced.
And they are probably going to want to keep some aside for the CTO.
You do not want a failure under your belt so make sure this is a winner before you consider taking it on. The fact that they don't have a viable product with customers already sold to concerns me greatly.
The short, sweet answer is advice I got from a mentor: talk it out until you're all happy. But I would caution against joining a company with founders who want to be involved "but have no distinct role in its next phase." If as CEO you're helping the company to grow and creating a lot of value, you may come to resent the fact that you only got 1/3 (or 1/4) of the pie. Clearly defined job descriptions (and a new vesting schedule with a cliff for the original founders) can ensure that everybody stays hungry and works hard to make the company profitable.
Unless you are sure the company will be successful, don't do it. Everyone and their mother has a "groundbreaking startup" nowadays. Even 50% of $0 ends up being nothing. Don't get blinded by being "CEO of a startup." Always take a step back and look at it for what it is.
If you ARE sure of the product, it really depends on what you're bringing to the table.