In any given reference frame you have a velocity vector that's some part space and some part time but has magnitude 1. It's just rotated.
There's nowhere to "stand still" in the universe. But if you pick a reference frame where you're moving less fast in space your velocity has more of a time component to make up for it. If you pick one where you move very quickly in space (maybe one that doesn't follow the Earth's orbit) then you have less motion in time. That observer sees you experience less time.
And if they pick a reference frame where you move the speed of light - where your velocity vector is fully in space; with '1' for space and '0' for time - they don't see you experience any time.
There's no way to stand still per se, but we can tell the difference between someone who accelerates and someone who doesn't - that's the resolution of the "twin paradox". So if one person travels around in a circle and their twin stays still (by magically floating above the earth without following its rotation, or by staying suspended at a particular point in the earth's orbit for a year while the earth goes around), then they have accelerated less than their twin and should therefore have aged slightly more.
What I don't understand is: does this still apply under General Relativity, or does proximity to the massive earth redefine acceleration?
There's nowhere to "stand still" in the universe. But if you pick a reference frame where you're moving less fast in space your velocity has more of a time component to make up for it. If you pick one where you move very quickly in space (maybe one that doesn't follow the Earth's orbit) then you have less motion in time. That observer sees you experience less time.
And if they pick a reference frame where you move the speed of light - where your velocity vector is fully in space; with '1' for space and '0' for time - they don't see you experience any time.