Conclusion
The next step would be to make a complete concordance of all mythologems of Greek religion, complete with cross references to their sources. I do not think that the methodology here is at all ambiguous. It is quite easy to recognise mythologems in any given material once one accepts that it is appropriate to look for them. The idea of a mythologem is scarcely new in principle, and all serious second-order mythographers, from Diodorus to J.G. Frazer have deployed it. What has been a great source of error has been the chief mistake inherited from the Greeks themselves, who in their desire to build a cultural history for themselves projected mythologems onto legendary times before the equally legendary Trojan War; we see these could not have belonged to that period, and we must infer they arose during the Dark Age and reflect the religious history of that age. It is this tradition of taking legend for fact that has unwittingly led to the denigration of the whole oral tradition represented by Greek mythology as altogether lying fictions. We see that the recent trend towards jettisoning the whole oral tradition and starting afresh with archaeology alone has been a much-needed corrective, and we can be heartily grateful for it, though it is now essential to go beyond that one-sidedness and treat the oral tradition with the respect it deserves.
Suicide of Ajax
Icon from a belly amphora by Exekias, c.530
Icon from a belly amphora by Exekias, c.530