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32N, 102W it is.

 I used Occult4 "https://occultations.org/observing/software/occult/" with this lat and long to get disappear and reappear times to the nearest whole second to generate the problem.  

I used my FORTRAN NOVAS with brute force to interpolate to the topocentric SD as LD at disappear time on the 35N line of latitude between 99W and 116W.  Then again for 45N. (Lats and Longs from dropping a big box into the Western US.)  Have an LOP by connecting two points, one on 35N and one on 45N.

Repeat for reappear time.  The two LOP's intersect quite close to 32N, 109W.  Iterating would have gotten closer, but I didn't bother.

Then, I worked on using Besselian elements and drawing curves on the fundamental plane.  Then projecting out to the sphere.  Intersecting a cylinder and a sphere.  Kept me busy for quite a while.  I used equations from "Explanatory Supplement to the Astronomical Almanac"  and "Spherical Astronomy" by Green.  I used a spreadsheet for manipulating and ploting the results. Again iteration could improve results.

Some figures attached. 

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