yah, the ring has to be thicker, and the pinion smaller, or they wouldn't fit the housing/carrier
The BEST way is make sure is to mark the ring gear, and pinion, and rotate the pinon while counting turns, the 5.12 will take 5.12 turns, or a little bit more than 5 turns, to turn the ring gear ONCE.
The 5.62's will be a little more than 5 and a HALF turns to get the ring around once.
That is if the third member is out and you can do that and see the ring
If the unit is still in the vehicle. Jack up ONE side of the rear end. Mark the pinion, or driveshaft, mark a tire (or brake drum ) and turn the pinion or drive shaft enough to spin a tire TWICE (to make up for the differential and spider gears)
The 5.62's are indeed rare. Your first clue is too look for a carburetor, unless it has a carburetor, you are probably out of luck.
The 1.3 looks very similar to an 8 valve 1.6. Check the gears, no matter what. Count em.. only way to know for SURE what you have.