#gai would likely assume that sakumo sacrificed himself on a mission to save a teammate

[soaringpigeonshovel]

Look. There is absolutely no reason Gai *must* know how Sakumo died. Neither Maito was at the funeral. The genin in Naruto's time somehow missed that the entire police force had been ctrl-alt-deleted. In fact given that Kakashi had clearly not heard 'your dad didn't do anything wrong' from anyone before Obito said it, even though the topic of fathers had come up between Gai and Kakashi before, i'd say that it might even be more likely that Gai didn't know when they were kids.

Which leaves the whole rest of the timeline for Gai to find out! And while the possibilities are endless, may I humbly suggest

Kakashi: "You know, when I died, I got to speak to my dad. It was... it was really great. We spoke about everything. I feel like a huge weight has been lifted off my shoulders, you know? I got the chance to tell my dad that I forgive him for killing himself."

Gai: "Your dad fucking w h a t"