What about $\gamma(x)$?

The expression for time speed

${ v }_{ t }= \sqrt {{ c }^{ 2 }-\cfrac { 2{ G }_{ o } }{ (x+r_{ e }) }  }$

is in the time domain.  Whereas x is measured from dense space to less dense space.  This velocity when multiplied by ${ t }_{ c }$ the standard time when time speed ${ v }_{ c }=c$ gives the duration of a second as experienced by a body at distance x.  Dividing by normal time speed c, we have an expression for time dilation.

$\gamma =\cfrac { { v }_{ t } }{ c } =\sqrt { 1-\cfrac { 2{ G }_{ o } }{ { c }^{ 2 }(x+r_{ e }) }  }$

As we move away from a gravitational field, time returns to normal time speed.  Inside the influence of gravity, compressed space, time speed is lower, as such time dilates when we leave the gravitational field and time speed increases.

This is time dilation.  Dividing distance in the space dimension by space velocity does not give you distance in standard seconds in the time dimension.  We experience time along the time dimension.

At distance far away from the influence of gravity, time is normal at time speed c, therefore $\gamma \le 1$.