The pinion shaft is the one the universal joint flange is attached to. You need to measure the movement of the ring gear, not the pinion. Use a magnetic base dial indicator or one with a C-clamp mounting attached to a long bolt screwed into one of the cover attaching bolt holes and position the stem of the dial indicator as close to 90 degrees from the movement of the ring gear as possible. Measure the amount of slack there is while rocking the ring gear forward and back. Unless the slack is WAY out of specification, don't mess with any adjustments. You are almost guaranteed to create a gear whine by changing the wear pattern the gears have established over decades of operation. I'd consider anything under .025" or so of backlash to be in the "DON'T MESS WITH IT" category. More than that- - - - -go shopping for another third member- - - -it's worn out!
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!