Interesting thought, breaking open a Time Atac pedal. Mine make the squeak a bit, too, but not all the time.
The problem is in the stainless steel ratrap springs and their "interface" with the brass cleats. Oil the cleats and see if that makes a difference. Look at the cleat and you will see under the protrusions front and rear where the rat-trap wires engage. Place a few drops of oil there.
I wouldn't go fiddling with the bearings and spindle unless you really know what's up -- it's a sealed bearing, and one pair of mine have not been serviced in more than 9,000km.