From your description, it sounds like it might be the same model I bought back in '69, when I was ready for a 'good' guitar.

It had two single-coil pickups, with a 3-way toggle switch. There was also a second set of Tone/Volume controls set into the pick-guard above the strings. This allowed pre-setting an additional voice for the neck pickup. The sound was a bit smoother than the Strats at that time; not as much 'quack', but a very good sound for blues.

The pick-guard was a white-black-white laminate, that had a greenish tinge to it.

The nut was unusual, in that instead of the string height being determined by the depth of the notches, there was a fret set into the fingerboard about 1/8" from the nut.

The neck was highly figured maple; rosewood fretboard with 22 frets.

The whammy bar was connected to a spring-loaded bar through a hole in the tailpiece.

If this is what you have, it was probably made in 1966 or 1967. There was a 12-string version called the SG-12. By 1968, Yamaha had moved on, to something that looked like an amoeba tied to a broken hockey stick.

That old SG-2 was one fine guitar. I eventually traded it in on a used Gibson SG. In hindsight, I should have kept the Yamaha. The Gibson was a piece of s***.