I have not seen or worked on the system you describe. My knowledge comes from manuals, not "hands on".
As I understand the system on these Dodge trucks, the speedometer takes its speed information from a gear at the rear of the transmission. If the speedometer did not have the adapter gearbox you describe it would indicate correctly in one of the two rear axle speeds, but be incorrect (by a factor of 1.391 which was the ratio between the two speeds in the rear axle) in the other one because the rear axle ratio changes after the point at which the speedometer gets its information.
They probably used the procedure shown of adjusting the cable with the axle and speedometer adapter both in neutral because both axle and speedometer adapter gear changes had a holding detent in neutral. Also using the middle neutral position will have less error in each gear than would result if the system were set up at one extreme of its travel and then moved to the other extreme.
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