Let me first explain what I mean. Take these two pairs for example:
付く、付ける (the first one is intransitive, the second one is transitive)
抜く、抜ける (the first one is transitive, the second on is intransitive)
(of course, つく has a lot of meanings/homophones, but this is a different question... or not?)
So, the question now becomes: is there a pattern here, or at least a statistics to try and predict without context if in a verb pair, say with ～く/～ける , which one is transitive and which one is intransitive?
Possibly this all just comes down to memorization, but who knows? I don't. Yet.
P.S. I tried to find if this has been asked before and found some partial answers: how to 'build' these pairs, whether all verbs come in such pairs, and even a very interesting and possibly related explanation about the history of okurigana and verb conjugations, but these are all... well, as I said, partial
Having created the question, I found three more related questions in the "Related" section: about etymology, about -eru/-aru verbs specifically, and about if there is a transitive/intransitive pattern in general, and so far it has proven especially informative for me:
-e(ru) - a kind of transitivity flipper, it can make transitives intransitive or intransitives transitive. An example of the first is さける ('split open', compare さく 'tear'), and an example of the second is つける ('attach', compare つく 'stick to').
Many of these pairs, とめる~とまる included, seem to have had these morphemes added to both members.
I'm not sure this is a grammatical process, at least any more; none of these morphemes are still productive as far as I know. You're probably best off remembering each word as a single lexical unit, especially considering the fact that there's a good deal of variation among what pairs up with what.
However, there might still be more information to this, or additional sources that the community might share