I always wondered what the instrument on the opening of this was. Sounded like a Sitar, but then also like an electric guitar. Turns out it's something called an Electric Sitar. Made by Danelectro.
https://en.m.wikipedia.org/wiki/Lady_Jane_(song)#cite_note-14[Brian Jones] no longer the principal musical force for the band, searching for methods to improve upon The Rolling Stones' musical textures.[12] He expressed an intrigue in incorporating culturally diverse instruments into the band's music, investigating the sitar, koto, marimba, and testing electronics. In the press Jones talked about applying the Appalachian dulcimer into compositions, although he seemed uncertain of the instrument, saying "It's an old English instrument used at the beginning of the century". The dulcimer was first brought to his attention in March 1966 when Jones began listening to recordings of Richard Fariña. The influence of these recordings would manifest itself in Aftermath, where Jones performed with the dulcimer on two tracks, "I Am Waiting" and, more distinctively, "Lady Jane". This later contributed to Jones's status as an early pioneer in world music, and effectively shifted the band from blues rock to a versatile pop group.[13][14]