You can't build a clock with a photon.

You can't build a clock with an electron either. You can build one with a muon though, since it will decay after some interval. It's not very accurate, but it's something.

In general, you cannot build a clock moving at light speed. You could build a clock with two photons. Measure the time by how close they are together. But if you look at the center of mass of this clock, it moves slower than light. If it didn't, the photons would have to move parallel to each other, but then they can't be moving away from each other, so you can't measure time.