Patio Potatoes

I know that flowering plants of potato is not really necessary for the production of potatoes (despite what many people think) but how do I know when to harvest if there is no flowers? Thank you!

Dieback is a good indicator of when the potatoes are ripe, but you can also consult closely around the plant and look for cracked soils. Gently dig in there with your fingers and you can find a small new potatoes.
"I used to fly one or two of each plant for a meal during the summer there used to be small potatoes there. I have never taken more than one or two of each plant.

The flowers are not the factor determining the time of harvest. When plants begin to wither and fall is when the potatoes are ripe and ready to dig.

When plants die and turn brown when it's the right time to harvest them. It is usually in the time of the fall.