both the amigasa and the hikosa zukin are seen at a three-day event, which is held just after o-bon. This is a time when people travel back to their home towns, have large family reunions and visit ancestral graves.
The festival dates from the 13th century when a priest called Genshin commanded villagers to dance in the Zao Gongen temple grounds to pray for a good harvest. The dance evolved into a folk dance and is accompanied by music and singing, which also evolved with rather agrestic and bawdy lyrics. For this reason, the festival was banned in the Taisho Era (1912-1926) but later revived and continues to be celebrated each summer.
I think amigasa is a catchall for hats made of woven straw (sedge), but I would like to know the names of the different straw hats as well, like 花笠 hanagasa. The hat pictured, I think, is a おけさ笠.
Having no idea what key words to use in searching for this hat, I Googled: Japanese taco hat.