The earlier 8.8 vehicles, would have had an ID tag bolted onto the diff cover in the Ford Pickups first around 1983 and up until 1985 those included four to five letters, no numbers. Ford then started phasing out the metal tags in around the 1986 models, replacing them with a sticker located on the axle tube by the brakes those will will have letters and numbers. The first number refers to the plant where it was built, and the next three refer to the ratio and type. The numbers can also tell you what car the rear end came in, though you need to look up the info online or in a Ford manual, as there are many codes. Without a Id Tag on the cover or Axle Tub you can not tell if the Axle has a Traction-Lok / Limited-Slip differential without removing the rear cover then it be identified by a large, S-shaped clip that's pressing on the side gears. The Factory 8.8 Gear Ratio's With Traction-Lok are: 2.73, 3.08, 3.27, and 3.55:1. All other Factory Gear Ratios are: 2.26, 2.47, 2.73, 3.08, 3.27, 3.45, 3.55, 3.73, and 4.10:1
You can also easily Id the Mustang 8.8 since most of the other 8.8s will have an offset pinion, but all the 8.8s in Mustangs have axles that are the same length on both sides. The 1986 to 1993 Mustangs have 29.063-inch axles, and the rear end is 59.250 inches from axle flange to axle flange. The 1994 to 1998 axles are 0.75 inches longer (the rear end is 1.5 inches wider overall at 60.750). The 1999 to 2004 is another 0.75 inches longer (the flange-to-flange width is 3 inches wider than with 1979 to1993 Mustangs at 62.250). If the rear cover is off than you can count the Ring Gear and Pinon Teeth and divide the Pinon into the ring Gear number for you Ratio. If the rear axle isn't opened up you can count the number times the driveshaft turns to that of the wheel.
Set the rear of the car securely on a good set of jack stands under the rear-axle housing put the transmission in Neutral and then turn one of the rear wheels. Watch if the other rear tire turns in the same direction if it dose you have a Limited Slip diff. In that case, you can leave both jack stands under the axle. If when you spin one rear tire and the other one rotates in the opposite direction, that means you have an open differential. In that case, you will need to remove one jack stand and set the other tire back on the ground.
An example using some tape reference marks
You could use a soapstone, chalk, paint, or tape etc. to make a reference mark on the tire plus also on the ground for use in counting the turns and also on the driveshaft next to one of the Case Ribs for a reference mark.
The Procedure for a Limited Slip type rear axle
You turn the tire one complete turn while also counting how many times the driveshaft also turns. Example if your driveshaft has made 3 3/4 turns, that would determine by a checking it against the available factory gear ratios that is a 3.73 to 1 ratio. Or if you had only gotten 2 3/4 turns, then you would have a 2.76 gear ratio.
The Procedure for an Open type rear axle
Because the open diffs will only turn half as many times when its lifted off the ground you will need to turn the tire two complete turns while counting the number of driveshaft turns. Again if the driveshaft turned 3 3/4 turns for two rotations of the tire, you would have a 3.73 to 1 Ratio. Or a driveshaft that only turns 2 3/4 times is a 2.76 to1 Ratio. Best of luck