Chris,
That's so cool that you have that memento of your Dad's! 
I have something a bit similar. It's a bracelet that looks like it's
made out of aluminum and has written on each link the VI corps campaigns
from North Africa through Rome. It also says "Don't forget me" and I believe
was made to send home to wives & sweethearts.
It wasn't my Dad's, but belonged to a Vet who'se family sold it after he passed away
because they thought it was "junk". Can you believe it? 
I bought it & wore it
for years in his honor and also in memory of my Dad. I stopped wearing it because
I began to worry that I'd lose it. It's now put away with all my Dad's army memorabilia.
I think you're right, by St Tropez they were so physically and mentally exhausted
they didn't care about keeping track of their whereabouts. Also - they were on
the move constantly.
Mary Ann