/start rant
THERE IS NO SUCH THING AS A PART-TIME CO-FOUNDER.

Sorry for shouting. But a co-founder is by definition someone who is fully committed to the company. So he/she cannot be part-time.

If you really want to give that person a title, you may want to try the term TOURIST-co-founder or WANNABE-co-founder

Now about the equity:

If you give equity to a tourist-co-founder you will have to explain to investors why you did that, instead of talking about what really matters. And this will be quite hard (read=impossible).

NEVER give any equity to tourists. They will make your startup un-fundable.
/end rant