It doesn't look like it's been mentioned in here, but the gear sets are also marked on the edge of the ring gear. That's how I found my 4.11 pumpkin in a pick-n-pull junkyard years ago. The dome cover on the other side of the banjo axle comes off easily, and it's then simple to use one tire to spin the axle until you can find the markings - as long as the driveshaft is disconnected or the transmission is in neutral.
From what I've read, the 3.90 gearsets were only used in one fancy trim level truck for one year, and are consequently incredibly rare. The 4.11s, while not common, are far more likely to be located than the 3.90s. If you want to get really ridiculously rare, try finding a Detroit Locker unit. They went out of production as soon as the Eaton axle design was dropped in the early 70s.
