It really depends. Generally, once big money is involved (500k ), you should both be full time.
I totally understand where you're coming from. Full-time co-founder here with my counterpart having a full time job (a resident physician at that!). It's tough but it works somehow especially since we are at the seed stage. But once we start raising real money (1M ) there's no way he'll be able to continue IMO. It can work but it's best if everyone is full-time.
I do know of a company with a co-founder who is also a resident physician and they just raised $3M. So there's a real-world example of it working out. And being a resident physician at a top-2 school is a much more difficult position to drop out of - there's no going back.
Most investors will ask for 100% time commitments but if you spread responsibility it can work (like the above scenario).
What matters most is: are you guys getting shit done? Are you making forward progress? Things can always be better and more efficient but if you're moving forward - keep moving.
You'll know when you need to propose the ultimatum to your co-founder. If there's money on the table and he has to quit, it's easier vs. the assumption (risk) of money being there.
Finally - add a few more players to your team. Offset the work to great people. It will not only make you more efficient but will show investors that people want to work with you. And they're committed to your product without having real cash flow. As a CEO, one of the most exciting things is getting great people to work with you. It's a great feeling and proves leadership. And some good 'ole fashion convincing. Good luck.