A few notes --
1. On every sideloader, there is a flat machined on the right side of the case below the output flange. The ring and pinion numbers are stamped in this flat, giving you the ratio with certainty. 38 and 11 = 3.45, 40 and 11 = 3.64, 39 and 12 = 3.25.
2. On early LSD's there is no white "S" -- the "S" is stamped in the case, on the right side above the flat where the ring and pinion tooth counts are stamped. The "S" is about 1/2" and may be sideways, angled, or upright (probably indicates whether Horst assembled it before or after lunch...)
3. The numbers cast in the case of the diff are not part numbers, they are casting part numbers. They will not help you identify the ratio, and you'll never find them in the parts book, microfische or ETK.
4. Given the age of most sideloader diffs, the "twist test" is unreliable. Most of the LSD units are only 25% lock, and once the clutches wear it's easy to turn them opposite.