Not all Cougars had inspection 'stickers' in the engine compartment. Not only the inspection stickers or paint daubs, but even the sheet metal is different! Really!
It all depends on where your Cougar (or Mustang) was built. OK, little history lesson here. Classic Mustangs and Cougars were built in three plants. Easy to tell which yours was built at. Look at your VIN. If the second digit is 'F' your car was built in Dearborn. If it is 'T' it was built in Metuchen NJ. (Unfortunately, I don't see too many San Jose, CA cars around here in Ohio so I am not certain of the code, sorry . )
Look at an original Dearborn car versus a Metuchen car, especially the front fender aprons, and you'll see that the Metuchen cars do not have the 'ribs' on the inner fenders that the Dearborn cars have. Different vendors or stamping plants, different parts!
One plant used paper inspection stickers, others used rubber stamps with paint. be careful. Don't 'cross-plant' your car!