I've done very little research on this simply because it doesn't seem like something that would be easy to find and it does seem like something better left for Russian natives, teachers, linguists, and the like. It was brought to my attention when I saw the phrase по его́ прика́зу in a transcript for this video. I then went to Wiktionary for more information on the word "по":
When I went back to the phrase по его́ прика́зу to check its case, I was a little surprised that prepositional case had not been used:
especially after seeing the example given here:
I even went back to the video:
to see if the transcript matched the audio. (It does.)
So, well, this confused me because if ever there was a time when по should take prepositional, I would think it would be in a phrase like "on his order." I resigned myself to just learning these as I go, when I got to wondering if there might be a way to make an educated guess with this word in the future. For example, if, most of the time, the dative is used with по when it means on, and I decline the noun that follows with the dative, I can expect to get it right most of the time and learn the exceptions as I go.