Does ぺこぺこ come from ''peckish''?
No. Its derivation is from purely Japanese roots.
ぺこぺこ is traced to texts from the early 1900s late 1800s (thank you, snailcar!). Granted, that's late enough to be an English-inspired term.
However, let's look deeper. Notice that this starts with a //p//. Historically, all of the modern //h// (and the /...