The story
Presumably from *whistful, from whist (“silent”) + -ful, based on older wistly. It is implausible that it derives from wishful, the required sound change being wishful → *wisful → wistful, which could not occur in Modern English, particularly not with wishful continuing in use. However, the sense of “longing” appears to be influenced by wishful, making wistful an ambiguous poetic word.
Etymology from Wiktionary, CC BY-SA 4.0.