What is the rule governing whether or not the reflexive construction is used? It seems clear with personal verbs like brushing ones teeth or cutting one’s hair, but not clear at all in the context of having sandals made.
There is no general rule. Some constructions in French require a reflexive construction. Some of those also do in English, some others don't.
For the example you quote, there is also a parallel to colloquial English:
"I have myself a pair of sandals made." -- Je me fais faire une paire de sandales.
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