I think the answer really is unknowable. Mind you, male pattern baldness is inherited via your maternal grandfather - so it’s plausible that the younger Gordian is bald and his father is not.
A few interesting research here : Henry Cohen wrote in 1885 about how to differentiate the two Gordians. He said free translation ) “We can recognize Gordian the old by the thinness of his face, his hollow cheeks and his aquiline nose. Gordian the young (...) has a bare forehead and we can’t notice any hair at all .” Cohen also quote Julius Capitolinus , who would be one of the writers of the ‘famous’...Historia Augusta. Between 312-334 AD. Look at what he said :”Gordian II was bald on his forehead.” But the most important information was given when Cohen quote Eckhel ( died in 1798 ) who explained the reason of Gordian’s baldness. He attribuated it “to his excessive love for women”........outch!
Thanks for referring to some of the original sources...not sure about that last point but who knows, in that case I am in trouble...
I would not call Cohen or Eckhel original sources, even if they wrote in the 19th and 18th century . Then Cohen misquoted Julius Capitolinus (or whoever wrote the chapter on the Three Gordians in the Historia Augusta): There is no mention of Gordian II´s forehead or hair in my edition of the Historia Augusta. What he does mention (The three Gordians, Chapter 6, 1.) is that the older Gordian had handsome grey hair, a broad face and a majestic expression. All Capitolinus knew about the features of the younger Gordian is that he had read in the work of Vulcatius Terentianus that Gordian II had the greatest resemblance with Pompeius, but was fatter than him (The Three Gordians, Chapter 21, 5.), and that the younger Gordian was equipped with a reproductive organ of such extraordinary size that people jokingly used to call him the Priapus of his time (Chapter 19.4).
If anyone is interested in an update: David Sear has just confirmed my theory that all three OP coins do in fact show Gordian I and not Gordian II (as advertised by the respective auction houses) and that in fact all genuine Gordian II´s of the type come from one single obverse die.
Thanks for the update; this has been a fascinating thread. I don't have either Gordian I or II in my collection.