Peaches like many tree fruits, will come off the branch when slightly lifted when they are ready to be harvested -- they will still be hard to the touch. Then I leave them single layer in a basket on the kitchen counter until the surface "give" ever so slightly when held -- THEN they are declared "ready to eat"
When they start *looking* like they are almost ready to harvest, it's a race against squirrels, chipmunks, and even groundHOGS

...so I used hanging (bird) scares and lengths of old garden hose, toy plastic snakes -- even recruited toy dinosaurs -- and arranged them in strategic perches on the garden fence and on the branches -- then gently held and lifted every day until they came off the branch.
(I DO have a very small young semi-dwarf plant that is only 6 feet tall -- your mileage may vary

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