[Saul] "having fallen" - "peson" NT Greek verb appears to be used for having fallen from a higher place [a horse?] to a lower place [the ground]
e.g., seeds falling from a tree into thorns below
Thayer's Greek Lexicon
STRONGS NT 4098: πίπτω
πίπτω; (imperfect ἔπιπτον (Mark 14:35 T Tr marginal reading WH)); future πεσοῦμαι; 2 aorist ἔπεσον and according to the Alex. form (received everywhere by Lachmann (except Luke 23:30), Tdf. (except Revelation 6:16), Tr (except ibid.), WH; and also used by R G in Revelation 1:17; Revelation 5:14; Revelation 6:13; Revelation 11:16; Revelation 17:10) ἔπεσα (cf. (WHs Appendix, p. 164; Tdf. Proleg., p. 123); Lob. ad Phryn., p. 724f; Alexander Buttmann (1873) Ausf. Spr. ii., p. 277f, and see ἀπέρχομαι at the beginning); perfect πέπτωκα, 2 person singular πεπτωκες (Revelation 2:5 T WH; see κοπιάω), 3 person plural πεπτωκαν (Revelation 18:3, Lachmann's stereotyped edition; Tr text WH text; see γίνομαι); (from ΠΑΤΩ, as τίκτω from ΤΑΚΩ (cf. Curtius, Etymol. § 214; Verbum, ii., p. 398)); from Homer down; the Sept. chiefly for נָפַל; to fall; used:
1. of descent from a higher place to a lower;
Englishman's Concordance πεσόν (peson) — 1 Occurrence πεσὼν (pesōn) Luke 8:14 V-APA-NNS GRK: τὰς ἀκάνθας πεσόν οὗτοί εἰσιν NAS: The [seed] which fell among KJV: And that which fell among thorns INT: the thorns has fallen these are...
My humble ignorant opinion from having horses for many years:
The horse was startled by the "flashed around light" [periastraphen phos] and threw Saul off [bucked him off].
I think that's reasonable.