Am I Missing a Grounding Strap For My Gas Tank Sending Unit?

Sorry, but it will... in most cases. Most of those bonding clips rotted off 35+ years ago.
And most of those cars, the gas gauges don't work. I can't count the A body's I've ran into where the gas gauge didn't work, and they were missing the ground strap. By adding the ground strap, voila the fuel gauge worked.

We could go back and forth until we are blue in the face on this subject. I'm not going to do it.

The Chrysler engineer's put the ground strap on for a reason.
That's good enough for me.