Both effects are actually correct, but they operate in different ways and can have opposite impacts on the perceived rate of a moving clock.
Time dilation is a consequence of special relativity, which states that the time experienced by an observer depends on their relative motion to the observed object. According to time dilation, as an object approaches the speed of light relative to an observer, time appears to slow down for that object relative to a stationary observer. This means that a clock moving towards you at near light speed would appear to run slower from your perspective.
On the other hand, the Doppler effect describes the change in frequency or wavelength of a wave (such as light or sound) due to the relative motion between the source of the wave and the observer. When a source of waves moves towards an observer, the wavelengths appear compressed, resulting in a higher frequency and perceived increase in speed. This is commonly experienced with sound waves from a moving vehicle or with light from a moving star.
In the case of a clock moving towards you at near light speed, the combination of time dilation and the Doppler effect creates an interesting situation. While time dilation causes the clock to appear slower, the Doppler effect causes the frequency of the light waves emitted by the clock (which are responsible for our perception of time) to increase, making the clock appear faster. The net effect depends on the specific values of the velocity and distance involved, and the two effects can partially cancel each other out or magnify one another.
To make precise calculations and determine the exact perceived rate of the clock, you would need to apply the equations of special relativity and the Doppler effect. These calculations involve the Lorentz factor for time dilation and the relativistic Doppler effect equation, which accounts for both the velocity of the source and the observer.
In summary, both time dilation and the Doppler effect are valid physical phenomena, and they can have simultaneous and opposing influences on the perceived rate of a clock moving towards you at near light speed. The overall effect depends on the specific circumstances and must be calculated using the appropriate equations from special relativity and the Doppler effect.