Snip purple wires to sending unit and mark where each wire goes.
Pop out metal float arm CAREFULLY.
Take sending unit off fuel pump bucket.
Sniff fingers cause they smell like gas...and laugh to yourself.
Lay backside of sending unit down on hard, metal surface.
Find a punch or 1/2" rachet extension that is as wide as the metal swivel the metal float arm snaps into.
Hit center of metal swivel with short, sharp hits with hammer until swivel tightens up a little.
Pop metal float arm back on and check swivel to make sure it moves back and forth freely.
Smell fingers again--because you love the smell of unleaded.
Once the fingers of the swivel have solid contact with sending unit and it swivels freely (but tighter than before), you are ready for reassembly.
Carefully pop metal float arm back off.
Strip wires back slightly and solder together.
Snap sending unit back in and pop metal float arm back on.

Aaaaaaaaaaand done.