I do alignments as a trade and I have a few ideas on how to start from scratch.
This method should work on at LEAST 67-70 model years. Perhaps similar for other vehicles with the Ram Assist Power steering systems where the control valve is seperate to the Center Drag Link.
The ideas I have in mind might seem complex unless broken into steps. Alignment work on any car, is nothing more than geometry, complicated by being muti-dimensional. With that in mind, so many of the things I might take forgranted as knowledge could seem condescending if written out or explained in what another might feel as too "detailed". Hopefully, these steps don't come across that way:
Step-1: Set the gear box & steering column as "centered"
*With the pitman arm disconnected from the PS control valve at the ball socket of the control valve, count the number of turns of the steering wheel it takes to go stop-to-stop and divide by 2. Turn the wheel back to "center" with exactly half the number of turns.
*If the steering wheel isn't upright and centered, get this corrected before going on to Step-2. The easiest solution here might be simply remove the steering wheel and centering it inside the car. Double check your results before going to Step-2
Step-2: Set the idler arm straight ahead
*If using a RESTORED assemblyline Idler Arm (new bushings pressed into an original part), it may be a good idea to leave the nut joining the two halves of the idler arm loose for this step. If NOS, OE Ford Service Part, it SHOULD be already correct. (Remember that Ford Service parts might look the same from other Ford Carlines so be 100% sure yours is a genuine Mustang Idler arm or that it has been corrected to work on a Mustang. More info about this detail in other threads). Assuming you have a RESTORED Idler arm, bolt it down to the frame (with a loosened nut joining the two halves) and tighten this particular nut ONLY after setting the idler arm to align with the centerline of the vehicle or after full vehicle is assembled and a road test confirms no other issues. DO NOT FORGET TO COME BACK & TIGHTEN if you choose to leave this loose at this time. I personally, would leave this loose until after the whole front end alignment work is done, tightening this particular nut, again... ONLY after confirming on a test-drive that NO OTHER ISSUES ARE PRESENT. Individual's choice if you think you can visually "see" or "measure" the centerline of your vehicle or not.
ADDED NOTE: Many aftermarket idler arms are NOT made like Ford made them, these are not as fussy in this particular step.
Step-3: Adjust the depth of threading the center link into the control valve
*THE HARD PART*
*With the control valve threaded in approximately 20-turns onto a bare-naked center (drag) link, (the assist ram and tie rods set aside for now off the vehicle), steering wheel locked in the straight forwards position (steering box centered already as a result of Step-1), loosely attach the Control Valve & Center Link as an assembly, without torquing down for ease in removing again if or as needed. Do not have the inner tie rods attached yet. The tie rods will be in the way if they are there, it would be best to remove them completely to keep them out of your way if these were already attached before this step.
*Confirm the "locked steering wheel" has not moved, visually look to see if the Idler Arm is in alignment with the centerline of the vehicle. The centerline of the vehicle runs from front to rear of the unibody structure and is an artificial point of reference. Adjust the turns of the center link into or out of the control valve as needed until the Idler Arm VISUALLY looks to be aligned to the centerline of the vehicle.
*NOW THE FUN PART! The fine-tuning: Once you feel you VISUALLY have the Idler arm centered, it SHOULD be checked for accuracy by taking measurements. Three-Dimension Geometry can be tricky but let's change our thinking to two-dimension and we can get this one down too with a simple tape measure. FIRST, assure yourself that the center/drag link runs parallel (crossways) to the body. If you have the WRONG Idler Arm or Pitman Arm, this step will not help until that is corrected. Remember, many items that LOOK RIGHT will bolt into your Mustang but not all that LOOK RIGHT are correct so this step should prove or disprove the correct pitman and Idler arms. So, with the center/drag link confirmed as parallel crossways, take a measurement from the center of the hole the Left Inner Tie rod would be inserted and measure to the center of the slot where the lower control arm mounting inner cam bolt. Check the right side using the same method as the left side. These numbers must be checked and confirmed in identical techniques and they ought to be 100% identical or again, adjust the center link or drag link as needed.
Once everything has been confirmed to be as close as possible, torque all fasteners and install cotter pins and find something else to do that has a little fun associated with it! (Some people suggest adult beverages, others might take the spouse out to dinner. Some might do BOTH!)
Ideally, these numbers and measurements should be double checked and in my opinion, all test-fitting and any adjustments needed to the number of turns on your PS control valve to Center Link, ought to be done very early on to the final assembly, essentially on an almost naked shell of a car, with no suspension components, no engine or transmission. Nonetheless, anyone might discover this demon the O.P. brought up at different progress points so these steps may assist you at any point of discovery. Getting this center link RIGHT early on will prevent a whole lot of later issues in overall satisfaction of the way your Mustang or Shelby handles while using the classic suspension parts.
I may need to edit this a bit but I need to get back out to the garage and get something done on my car so I hope this helps some people see the picture better at least.