Books on projections, coord systems
Whatever you did to identify the problem is a key learning objective for those who haven't and should be part of the workflow.
How did you do that?
The blunt answer makes me look smart, but that's not real fair. There was a fair amount of "reasonable guesswork" applied.
I took the nomenclature "true north", and saw the lines drawn on a globe, that converge at the poles of the earth.
And, I saw the term "Grid" in grid north, and saw non-converging lines.
Overlaying these 2, I saw theta, or convergence.
Then, I struggled mentally with these 2 superimposed images, and realized we are shifting the "backsite", not the "foresite".
Thus, a grid bearing will have a higher azimuth number, if I'm west of the central meridian, (which is where "true" or geodetic bearings are the same). Than a true bearing.
Laplace correction was not significant, for my purpose, as my instrument was not that caliber.
So, I've been using grid bearings, with solar observations, for well over 35 years.
My sun shot software allowed me to compute sunshot, with both grid brgs and geodetic brgs.
But, even before I had that, I used to compute sunshots, with scaled lat longs from a USGS. quad sheet. I'd artificially do the shots twice, once where I'd taken it, and once at a place 1 mile east, or west, to approximate convergence. This way, I could run an open traverse, and close the angles against the sunshots. This gave me specific convergence, for that area, or lat/lon.
My little brother was taking the ICS (International Correspondence Course) at the time. We used to talk alot. He taught me those big words, like theta, and how to break down section 5, 6 and 7, (when I could not remember what dad had taught me.) Also, Single Proportionate Measure, and Double Proportionate Measure. (SPM, & DPM).
So, when I first got RTK GPS, I bought a used Topcon Legacy E for 25k. I brought it home from Blue Eye Missouri. I took it to another surveyor, (TDS data collector), and asked how to get it to generate GROUND SCALE and GRID BRGS. It could not do this directly. It was a 2 step process. Set it all up, ground scale, and geodetic at the base. Then, go look up convergence, then go reset the prev system, with theta applied.
This I suspect is where most surveyors missed the issue. So, this other surveyor immediately replied "Is this why when I move my base, and back shoot, to my previous base, that there is a little rotational problem?" Well, we went over it, until we both learned. I learned how to do this in the data collector, and he learned the same, and why algebraicly subtracting the geodetic brgs, gave convergence difference.
Well, before this, I'd been using LOCUS GPS. These were 8 channel, L1 only units, that had algorithms to use the lowest sats in the sky.
So, I had tons of jobs, on grid brgs, ground scale. This was why I needed my legacy e system to address this.
Anyway, I'm no genius. I'm intensely practical, and useful, to equip others, (sometimes) by skipping alot of sidetracks.
IF I can once visualize and learn, I can often help others, by skipping alot of peripheral stuff.
Anyway, I'm now a Javad user, as their approach is a real neat screen, that allows all kinds of controll over the way this issue is handled. Not to mention it's ability to flush out genuine data, in rough places for GPS.
So, that's my story, of how I got this way.
Time to wake the kids.
Some students, it's better to present the problem first, then the math.
Academics tend to present the math.../theory first.
If you present the problem first, then it builds a shelf in my brain first. If you present the math first, then I have a scattered pile of disorganised facts.
Some people can do either, or both. I prefer shelves first.
If you are looking for a Handbook type publication, this is quicker and easier to reference than any of my textbooks on projections, SPC or convergence.
If you can get your hands on one of the old NAD27 books for your state, those are full of information explaining how to. Working through "hand" calculations from field observations to geodetic conversions.
Nothing beats doing it with pen and paper.
I find it amazing how many excursions into 1980's era government publications people are wiling to do to avoid spending $73.02.