That's an interesting interpretation but a quick search didn't turn up the first version of that until 1861, so it seem rather late to have influenced EO iconography. Perhaps you are familiar with earlier examples of that interpretation?

Impetuous or not, Peter was likely influenced by the many decisions made by lots in the Hebrew Scriptures. e.g., picking a scapegoat (Leviticus 16:7-10), assigning priestly duties (1 Chronicles 24), dividing land (1 Chronicles 6:54), etc. Furthermore, Proverbs 16:33 & 18:18 indicates the outcome of lots is from God and reduces conflict.

Anyway, ascribing random processes to the divine for decision making, particularly political situations seems to have strong textual support within the Judeo-Christian tradition. I'm curious about parallels in Islam and other offshoots.