I'll keep it nice and simple. On a world that does not rotate is it possible to have a mountain that is high enough that when you sit at the top, you can see the divide between daylight and night that spans the planet? If so, how high would it have to be and could a human survive at the top without a spacesuit?
How big is the planet?
Picture the solar latitude, by which I mean the latitude based on the current sun’s angle, not the planet’s pole. The circle of that latitude line is the size we care about. The elevation needs to be high enough to see antipodes of that circle. (Note: This is the meaning of opposite that allows the problem to have an answer. If you meant viewing the antipodes of the planet as a whole, you would actually see the entire terminator if you located the mountain at the equator so you would not speak of two points; and it cannot be done.)
Clearly it gets smaller with decreasing distance to the solar pole. In fact, if you’re at the (solar) pole, you will see half light and half dark on the ground at your feet. So, zero, for some choice of parameters that you did not specify.
More generally, determine the distance to the horizon for a mountain of some given height and planet size. Locate it far enough toward either pole so the opposite sides of the terminator are within this distance.