Any ideas on how to doodle something that sounds at least remotely like one?

Check bank 4 of gmlib, there's probably already an instrument that fits your need:
https://www.lexaloffle.com/bbs/?tid=54906

If it's alright I'll plug my wavecatalog: https://wavecatalog.neocities.org/ (need to keep updating it...)
Not sure if it's quite electric guitar but candle might be nice:
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