I have grown potatoes for many years as well as my folks since generations back, and there is many types of potatoes that all have their own ideas of when they are ready. Unless the soil is too wet you can keep them down there well after the plant itself have gone try and wilted. But in warmer climates I guess they can start to grow themselves and that is to be avoided.
One can pick the tubers almost from they first start to form, but when small they are a bit of a wasteful delicacy

@GoblinQuester Thanks for the tips that really makes sense actually we are learning about potatoes from this wonderful thread. We will focus on checking the size and skin instead of relying on flowering, and be more careful with fertilizer as you mentioned.

And of course I farm them in a cold temperate climate, which is quite different from the circumstances you have, but the good thing with potatoes is that they are quite forgiving as a crop, and you can save some as the seed for the next year (although that differs also with type how good result you'll get).

@GoblinQuester You are absolutely friend. Tbh, we found these potatoes already growing on the land. As you know, we recently bought land, so they were just beginning to germinate. We hav done our best to care for them and and now look at how healthy they are they really look wonderful additional we are still learning more about them! 💪

That is the fun thing with buying a old property, all the things you discover from the previous owners. I buying an old house right now ... a "project" and having fun exploring the gardens nooks and crannies.