Gravity decreases with distance from the Earth’s center. The lower the gravitational potential (the closer the clock is to the source of gravitation), the slower time passes, speeding up as the gravitational potential increases (the clock moving away from the source of gravitation).

For an object which is accelerating time passes slower. But an object on a mountaintop isn't accelerating, because the mountain has an upward counter-force.

What am I missing here?

This is because of relativity and the fact that there's more force at in the valley than the mountain.

https://en.wikipedia.org/wiki/Time_dilation

What about the fact that you are moving faster when on top of a mountain than in a valley due to the rotation of the earth and being farther from the center of rotation?

Does this also have an effect on your relative time?

Yes, it makes the equipotential surfaces of Earth's gravitational field (the surfaces on which time ticks "at the same rate") ellipsoids instead of spheres. The "geoid", which is the standard such surface that defines UTC on Earth, is the equipotential surface that averages to the Earth's sea level, and is 13 miles further from Earth's center at the equator vs. the poles.

Relativity: The Special and the General Theory (1916) Einstein, Albert

https://www.abebooks.com/9780517884416/Relativity-Special-Ge...

That's a 404, sad.

I'm guessing it's relativity doing its job.

gravity?

They did, about 108 years ago.