The timing for harvesting potatoes is a bit different here in Hawaii than back in NJ. When I first started out I waited for the plants to die back. Turned out to be poor timing because the mice got them all. So I tried checking the tubers earlier, hoping to get baby new potatoes that weren't half eaten by the mice. What I discovered was that I could get a nice crop by harvesting earlier than I had be led to believe.
As soon as the plants "look tired", I harvest the taters. By "look tired" I mean that the plants are no longer bright green and standing perky. The leaves tend to dull. On some varieties the leaves will droop or curl a bit. The plant tends to sag a little all over. Thus, it looks tired. A few varieties might bloom, many do not. So I can't judge by the blooming cycle.
Once the plant looks tired, I will remove the mulch, often revealing several tubers near the surface. Any that have greened I will pick and set aside for propagation rather than eating. I find that it is easier to pick those greenish ones now before digging the rest. I'll also pick the tiny "rejects" and toss them into a different pile. They will go to be cooked for the animals.
Now I'll pull up the plant and take a shovel to unearth the buried tubers. This variety is Red Gold. It's not the heaviest producer I grow but it gives me several nice useable potatoes per plant.
Some potato varieties are ready for digging in two months. Others at 3 to 4 months. They come to harvest faster during the summer than during the winter. And they can be grown year around here.
I've been asked if I've ever tried growing potatoes in a barrel, a compost pile, atop the soil under a thick mulch, in a trashcan, etc. No, I haven't. I did grow them once in one of my pallet boxes and it worked out just fine. But I have great success growing right in the ground here, which I find to be very labor friendly. So I haven't put the effort into trying other methods that would be more time consuming or require more resources.