This is the source of the canon Squeal: a little flywheel and geartrain on the right hand side of the mirror box in the Canon AE1 and all the rest of the A-series Canons. With the top cover removed from the camera, it's possible to sneak an oiler needle down from above and reach the mechanism. BE CAREFUL, AND DON'T OVER-OIL IT! (The "Tomosy" reference is to Thomas Tomosy, Camera Maintenance & Repair, which also discusses this and other problems. I highly recommend this as well as its companion "Book 2".
Of course, before you can do the above job you have to get the top cover off. Here are sketches for removing the top cover of the AE1 and the AE1-Program. The AE1 is trickier, look at both sketches for it before starting.
Sorry, I don't have sketches for the top cover of the A1 or the other A models.
Good luck! You're on your own from here...