Gravitational time dilation does not exist because, in a gravitational field, light falls as posited by Newton's theory:
James Hartle, Gravity: An Introduction to Einstein's General Relativity, p. 113: "If we accept the equivalence principle, we must also accept that light falls in a gravitational field with the same acceleration as material bodies."
Paul A. Tipler, Ralph A. Llewellyn, Modern Physics: "A beam of light will accelerate in a gravitational field as do objects with rest mass. For example, near the surface of Earth light will fall with acceleration 9.8 m/s^2."
This implies that the variation of the speed of falling light is proportional to the variation of frequency (proved by the Pound-Rebka-Snider experiment):
Max Planck Institute for Gravitational Physics: "You do not need general relativity to derive the correct prediction for the gravitational redshift. A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices...The gravitational redshift was first measured on earth in 1960-65 by Pound, Rebka, and Snider at Harvard University..."
R. V. Pound and J. L. Snider, Effect of Gravity on Gamma Radiation: "It is not our purpose here to enter into the many-sided discussion of the relationship between the effect under study and general relativity or energy conservation. It is to be noted that no strictly relativistic concepts are involved and the description of the effect as an "apparent weight" of photons is suggestive. The velocity difference predicted is identical to that which a material object would acquire in free fall for a time equal to the time of flight."
Variation of the speed of falling light as per Newton's theory implies NO GRAVITATIONAL TIME DILATION.