Your pressure gauge may not be accurate. First I would change the pressure gauge (it's cheap).
Then turn off the power to the pump and drain all the water to "0" pressure. Then add or reduce the air on the tank air valve to 33 lbs (if your pressure gauge is actually reading 35 lbs cut on and 60 lbs at cut off). The air pressure in the tank should be 2 lbs less than the cut on pressure. This should fix your instantaneous no pressure.