gnashing,
The base plate is held on by a couple of cross point screws.
There's nothiing tht's going to fall out by removing the cover.
I've got an AE1 body in front of me now. There are two magnets visible when you remove the base plate. The smaller of the two is the one that controls the closing curtain. You will be able to clean the mg. surfaces without disturbing anything else.
If you would like to do a more thorough job,REMOVE THE BATTERY. Unsolder the red wire leading to the coil from the front of the camera, remove the 2 crosspoint screws holding the mg assy in place.
clean the mg & armature surfaces with alcohol NOTHING ABRASIVE & reassemble.
It wouldn't hurt to hit the red & blk connections with a soldering iron also.
If that doesn't fix it it may need a new coil or the problem could be in the circuit board.