Before he graduated to a real Sitar, a buddy of mine had one of those old Electric sitars
As I recall, it was a pretty straight ahead guitar except that the bridge was a flat rectangular block of very dense wood or maybe metal with no notches, so the strings lay across the whole width of it. That made the strings buzz with some high overtones.
It had some sympathetic strings, but because it was an electric you never heard them much unless you strummed them. I thought that part of it was kind of bogus.
The other thing was to put really light gauge strings on it, because on a real sitar the frets are suspended in 'mid air' so the notes are really bendy.