A gas lift valve is opened and closed by subjecting a pressure-sensitive piston to pressure differentials between annulus and tubing pressures. The piston can be held in (and released from) a closed position by rotatably indexing an indexing assembly in incremental rotations on the piston when in the closed position. The indexing assembly is rotated when the piston is alternatingly moved in opposing axial directions when the pressure differential is alternated. In response to those incremental rotations, an outer ratchet on the piston can be alternately expanded and contracted. When expanded, the outer ratchet engages a ratchet profile in the gas lift valve to prevent the piston from moving open. When the outer ratchet is contracted, however, the piston can be moved open.