The wiper motor attaches to the wiper transmission which links both arms together. If only one works the transmission broke, as there is no way to disconnect only one arm. One arm may be stripped on the post, but either way the whole thing gotta be replaced
Both posts are attached to the transmission arms by rivets. If the clip fell off the motor, nothing would move.
Good news that is a easy junkyard find for $10 or so. All the bolts should be accessable from the cowl vent area. You can figure out how to do in on the junkyard car before touching your stang at least
P.S.
I've had 3 wiper motors crap out on me, lotsa fun. Maybe should grab the motor from the boneyard car too. You'll notice lots of em are missing the motor. Maybe easier to grab the trans from one of those. It's nice when a victim is already partially disassembled.