Forget those investors for a minute.. you dont need to approach them for 6 months atleast i think regardless of what ure doing. Ask the guy to put enough cash in the company for 6 months on day 1. If he does that, its automatically in his interest to get investors and work hard.
If you are unsuccessful in getting investors, its more likely that the product sucks, not the co-founder.
About the equity:
Lets say hypothetically he leaves you 1 month after you guys started..You can manage your living expenses but no money for marketing / promotion etc. You probably have to turtle up and cut almost every expense.
Will you be able to launch a beta and do sales yourself in such a position ?
If yes, then you probably dont need him that much. But if he is the only one doing sales then you need him a lot.
I would also suggest that if possible ask a common friend to answer those equity split questionnaires for you. Often we will give ourselves more credit than we deserve. You got 67% that tells me you probably ticked a lot of boxes relating to sales.
If you redo that survey and attribute all sales effort to the other guy, the answer will come out that he should be CEO.. and trust me , often that's the truth.. The guy doing the Sales ought to be CEO.
So answer this.. who does the sales.. and can that person continue doing it if the other guy leaves him ?