Of course it has to be a function of g.

No it isn't. See this depiction of gravitational potential:

CCASA image by AllenMcC, see Wikipedia.The time dilation is represented by the depth of potential, how low in the plot you are, whilst g is the slope of the plot. Note that there's an inflection, so g at one elevation is the same as g at another. You can find two places on the plot where you can draw the same tangent.

If you are stationary on the earth you are experiencing time dilation.

Yes.

You are not accelerating away from it.

Yes.

The velocity involved in escaping the field is due to kinetic energy.

Yes, and in your ascending rocket going faster and faster you are swapping gravitational time dilation for special-relativistic time dilation.

If the gravitational field were absent the time dilation would be due to the velocity.

Yes.

At a stationary position on the earth there is still a potential for acceleration. However there is NO potential for escape unless there is an impetus away from the surface. This will INDUCE a time dilation.

Yes. And as you ascend away from the surface you reduce the gravitational time dilation.

Without the impetus there is no dilation due to Ve. Can't you see that?

Yes.

You only have the value of g operating.

The acceleration due to gravity is g, and it is due to the

*local slope* of the potential. That's like the local slope of the gravitational time dilation. If your clock at the ceiling runs at the same rate as your clock at the floor, your pencil doesn't fall down. If your clock at the ceiling runs faster than your clock at the floor, your pencil falls down. If your clock at the ceiling runs much faster than your clock at the floor, your pencil falls down much faster. Note that your clocks might be light clocks, and that g can be expressed as the local slope of your plot of the coordinate speed of light.