George,
There is always more to learn, but it appears the equal length hinge was introduced around Aug 1924. The earliest equal length hinge in the thread discussion at:
http://www.mtfca.com/discus/messages/80257/114100.html had an engine number #10,377,xxx and belonged to Dan Treace at the time. It also had the wooden door post. Note I believe Dan had a type-o in his post when he said it was built Aug 16, 1924. Bruce McCalley's engine serial number log shows "no engine" numbers assigned or stamped onto engines on Aug 16, 1924. But for Aug 26, 1924 they had engine serial numbers 10,375,722 to 10,382,721 produced (or the number sent to a branch plant that assembled engines and stamped that number on the engine they assembled).
Note --- Ford did not really like "model years" but General Motors used them to sell new models quite successfully. Based on the current information I have seen so far, I believe that equal length hinge was basically a one year item "in USA production." I.e. Aug 1924 to Aug 1925 when the 1926 Improved Models were introduced in the USA. From the posting listed above, the equal length hinge was apparently used as early as Aug 1924. It may have possibly been earlier -- but I don't have any supporting documentation on an earlier use. If anyone else does, we would welcome that data point.
I suspect that some plants in other parts of the world began producing the 1926 style open cars later than the USA. And "IF" those plants in other countries continued the USA 1925 style body -- then they would have continued the 1925 style hinge longer.
Note the price list of parts was mentioned above but it does not always answer the question in a nice clean manner. For Mark -- from Bruce's Encyclopedia he has:

- Equal length door hinge.jpg (29.22 KiB) Viewed 5163 times
And from that -- I don't have time to figure out why they list the same door hinge for 1912-1917 in the 1917 price list of parts. Perhaps Bruce made a type-o? Or perhaps they used the same factory number for the part and figured the owner would list the year of the car and they could then supply the correct hinge?
But the Sep 1920 price list of parts has factory number 5297 fitting 1914-1920.
The Dec 1921 price list of parts has it fitting 1914-1921 (again if they were using "model year it could have said 1922 -- but that is a different question)
The Sep 1923 price list of parts has it fitting 1914-1923.
The Mar 1927 price list of parts has it fitting 1914-1924 [NOT 1925]
Note in the Apr 1925 price list of parts a NEW FACTORY number 20022 in used and is listed as fitting 1924-1925.
The Mar 1927 price list of parts has that same Factory number 20022R (R for replacement) and still listed 1924-1925.
Note the MTFCI (International) Judging Guidelines 7th Edition list the equal length door hinges for the 1925 and not the 1924 year cars.
I suspect that in Aug 1925 there were some cars produced with the older style hinge and some produced with the newer style hinge. And the ones with the older style would be looked at as 1924 models and the ones with the later style hinge would be considered 1925 models using that judging guideline.
I do not know how long that overlap lasted.
Not requested -- but some advice offered for free and maybe not worth that much. If your friend is restoring the car for Stynoski competition, and it is an early 1924 car (i.e. before Aug 1924 etc. I would recommend the 1914-1924 style hinges unless he has documentation supporting the equal length hinges that early. Note there may be a Factory Drawing for Factory Number 20022 at the Benson Ford Archives. If so, it may have the original date the part was drawn up. And normally the parts are NOT produced before the Factory Drawing is made telling the folks the dimensions etc. of how to make the part.
If they are working towards a good driving T -- either hinge will work with car and door.
Respectfully submitted,
Hap l9l5 cut off
Minor Rabbit trail: Did the C-Cab Ton Truck use the same hinge as the open cars? If so then the hinge continued into calendar year 1927 when the last 91 C-cabs were produced (ref page 173 of Bruce's book "Model T Ford.")