I need a little help on deciding between PP arguments and Adjuncts. Here are the few sentences I am having trouble with.

We can't account for the missing money - adjunct?

That reference pertains to the civil war- ????

I cycled to the river- PP argument? indicating location

what types of evidence/tests could I use?
Shall I assume you are using the term 'PP argument' to mean a prepositional phrase which is an argument of the verb, i.e., a required element of the sentence without which the sentence makes no sense? I'll make that assumption.

(I get the impression that you yourself aren't sure what the terminology means.)

We can't account. - nonsense - The PP "for the missing money" must be an argument.
That reference pertains. - nonsense - The PP "to the Civil War" must be an argument.
I cycled. - possible - The PP "to the river" must be merely an adjunct.

Thank you I wasn't quite clear on the two before and now I understand.