Thank you Michael

WOW!
The script works perfect on the sample scroll curve.

(Limited planar YZ testing.)
The script will work from command line, or as a shortcut key, if there is only one curve in the 3dm.
If there are two curves, only one curve receives tangent points. Which one seems to be related to which of the two curves is "Active."
Selecting the curve does not change the "Active" curve.
Deleting the points, and re-running the script just creates the tangent points on the same curve.
It is possible to get the "Active" curve to switch to the other curve, by deleting the active curve.

Starting from a blank screen geometry:
Draw a line. The script does not produce any points (Good).
Add a circle. The script does not produce any points, because the line is at the top of the "curve list". (OK)
(I do not know what the "curve list" is.)

Erase all of the curve geometry, and draw a circle, then a line. The script works perfect on the circle. (Good)

Erase all of the curve geometry, and draw a big circle and a small circle. The big circle is at the top of the "curve list", and the script finds the 4 tangent points for Y and Z direction. (Good).
Picking the small circle does NOT bring it to the top of the "curve list".

So maybe add some "pick curve" dialog, and somehow place the curve at the top of the "curve list".???

- Brian

Having other existing points does not seem to have any detrimental effect.
Having a hidden image does not seem to hurt either.
Hiding the "active" curve (circle) does NOT reduce its "active" status. The script will still find the same tangent points.

Will try some more curves, 3d and other planes...

- Brian

I assume that tolerance reduces the number of candidate tangent points to less than "infinity.":-)