There is an introduction to this in herethis article from the University of Victoria Study Zone, but an introduction is all it is.
Reflexive pronouns are used after many verb + preposition combinations [where prepositional object and subject have the same referent!], such as those that follow ...
[and only 4 examples are provided!]
KÖNIG AND GAST go a little further in attempting to rationalise the situation:
1.1 Optional reflexives In contrast to German, reflexive pronouns are optional in cases like the following:
(9) a. John saw a snake near him/himself.
b. Mary pushed the brandy away from her/herself.
c. Liz wrapped the rug around her/herself.
d. Bill pulled the blanket over him/himself.
Even though the self-forms in examples like (9) may find their antecedents within the same clause, such forms are not obligatory, but can freely be replaced by the corresponding personal pronouns, possibly with a slight change in the perspective expressed....
1.3 Unexpected personal pronouns Among the peculiarities of English also the following structures have to be listed:
(11) a. John did not have any money on him (/*himself).
b. He likes having children around him.
c. Mary has a whole week of travelling before her.
d. Mary put all her problems behind her.In sentences such as these reflexive anaphors are excluded. As in (9), the pronouns relate to an antecedent within the same clause and thus do express co-reference. In contrast to (9), however, the prepositional phrases containing these pronouns can in most cases not be regarded as co-arguments of these antecedents. Moreover, semantically, co- reference is the only option here. The pronouns in (11) cannot be replaced by or coordinated with other noun phrases, nor can they be stressed. In other words, Mary cannot leave her problems behind somebody else and John cannot have any money on Bill.
However, it is probably not easy to distinguish many cases where reflexives should be used. In such cases, it is best to check unfamiliar usages on Google (eg I have some "money on me" v "money on myself"; "Look after yourself" v "Look after you", disregarding false positives "I am going to spend some money on myself"; "Mary will look after you" etc). Dictionaries may include helpful examples.
Sometimes, a reflexive pronoun may be substituted for the more natural non-reflexive one for emphasis ("For me/myself, it's about the way I carry myself and the way I treat other people.")