My guess is that the counter and water on it are slightly warmer then the shot glass. What this does is first traps air inside the glass since it is wet. Now the glass heats up and with it the density of the air decreases and expands because it too is warming up and some of the air escapes pushing the glass. The air escaping is not easy to see but I would wager that is what is happening. I had a glass of ice water move like this once.
Edit: I am also guessing your counter is slightly not level and that is why is goes that way. The air escaping you won’t really see it is ever so slight like the shot glass burping and lifting ever so slightly on one side and the glass moves then.
That seems to make sense! I assume the delay between each movement is due to the time it takes for the air to expand again enough to forcefully escape from the side of least resistance (where the counter is ever so slightly higher).
I would assume it's because the water decreases the friction needed for the jigger (the 12 year old in me thinks that's a funny word) to move across the non-level surface.
