[When a Sheep Is Due for Involuntary Arousal]

Answer—and Allah knows best: What appears—Allah knows best—is a distinction: the movement that occurs at times of fatigue, relaxation, and the like does not require anything, because warding it off lies outside a person’s power: “Allah does not charge a soul except [with that within] its capacity.” [al-Baqarah:286]
As for the movement that does require a blood-sacrifice, it is that which arises from deliberately procuring its causes, and not otherwise. Thus, if arousal occurs without a deliberate cause, nothing is due—per His saying, “And there is no blame upon you for that in which you have erred, but [only] for what your hearts intended.” [al-Aḥzāb:5].
The proof for the matter is His saying, “So whoever has made ḥajj obligatory upon himself therein, there is to be no sexual relations (rafath), nor disobedience, nor disputing during ḥajj.” [al-Baqarah:197]. Rafath is intercourse and its preludes; so if arousal occurs because of those preludes, a sheep is due.
Those preludes are: looking with desire, kissing, fondling, embracing, and the special speech that occurs only between spouses. If arousal occurs for some other reason, then nothing is due.
This is what has appeared to me. Allah knows best, and praise belongs to Allah, Lord of the worlds.
Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.1