It’s as simple as you working part-time, and you shouldn’t overthink it beyond that. You charge them whatever you have to, and any longterm bonuses in the form of equity is basically there only to motivate you to stick around longer than you in most cases will want to (web search: cliff vesting).

What I do is that I start as a paid advisor, which essentially is a paid discovery phase. Then I slowly take on the responsibilities of a paid CTO. And only if all that works just fine I’d be willing to discuss equity as a way to keep me around (or to lower my salary).

That being said, personally I really want to work with very early founders as that’s where I can do the most to help, but that means that they’re also very inexperienced (which causes huge problems, and lots of arguments). So I’ve ended up having to focus on them paying my regular consulting fee from day one simply to weed out the too unprofessional dreamers. So if you’re being approached by more mature and professional teams, and get good terms, equity might actually have more of a real world value; just remember that it most likely has zero value until the day you’re able to actually sell it, so have a realistic plan for how to do that.