Thank you to the ham radio guys with a post from 2008 about this.

Check the gas cap. There’s a dial labeled “on” and “off” that you can turn. It can (and will) let you be halfway in between the two as well, which will let you get some fuel but not enough to keep it going. Turn it all the way to ON. I found this out the hard way and had dismantled and cleaned half the generator already. Oops.

honda e2000i fuel cap