They will continue to ripen off the tree.
As far as tasting good it depends a lot on the variety. There are astringent varieties which taste like edible desiccant trying to mummify you from the inside out. These are fuyu persimmons which are not astringent. They’re crunchy kind of like an apple but very mild flavored. Personally I like them fully ripe or even ripened and dehydrated.
For me to get to enjoy them they have to survive the deer and my wife; I’m not expecting to get any this year 😅
























Wild persimmons are tricky since they have to be sooo ripe to be palatable.