I haven't listened to the particular song that you are speaking of but a friend of mine used to play some Indian classical (Carnatic) music on his guitar. His tone was very sitar like.
I remember that he used to use thin gauge strings on his Les Paul and tuned down atleast a whole step. The strings used to feel pretty flabby but he used a lot of heavy sliding (distinctly beautiful technique he had). I guess part of the trick is that when you pick a flabby string, the pitch bends initially like a sitar's attack. Also your slide and vibrato will be critical as Indian classical generally uses wide and slow vibrato as opposed to the more subtle vibrato in western music.
He also said he used some kind of a phaser/flanger, though I am not quite sure how. The effect was not distinctly audible (try less depth/effect mix, not like jet plane phase/flange).
Also, try tuning the guitar so that you have open strings in the root and 5th of the key you are playing. Another thing that could help may be a very subtle mix of an +1 or +2 octave up effect if you have a pitch shifter.
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Guitar: '98 MIJ Ibanez RG520 QS w EMG 81/60
Amp: Laney LC15R Tube, Fernandes 20W SS
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