I don't have access to the book to get the exact quote
Google Books is your friend:
Is there anything to this?
Your cousin got the anecdote slightly wrong. Collins did not report that the soldiers were Nazis (a technicality perhaps) nor that they cut off their own eyelids.
Collins didn't actually claim to have seen this himself. In this extract, he doesn't explain what evidence for motivation was found by the two guys (or perhaps the men from the 101st and/or 82nd who told the two guys) nor does he explain how they distinguished other causes of the injury from the cause they suggest.
I can't find any other sources that mention German soldiers being deliberately mutilated in this way.
There is the history of Johannes Steinhoff a German pilot who was burned in a crash and had to have his eyelids reconstructed after the war. It is difficult to see how this could be the origin of Collins' anecdote.
The idea of cutting eyelids off as a punishment (not as a means of preventing sleep) goes back a long way (e.g. Roman stories of the torture of Regulus in Carthage).
A possible origin for stories of this sort could be reports about the effects of severe cold on German soldiers at the russian front:
The Italian journalist Curzio Malaparte recalled in his novel Kaputt how he had watched the German troops returning from the Eastern Front, and was in the Europeiski Café in Warsaw when "suddenly I was struck with horror and realised that they had no eyelids. I had already seen soldiers with lidless eyes, on the platform of the Minsk station a few days previously on my way from Smolensk.
"The ghastly cold of that winter had the strangest consequences. Thousands and thousands of soldiers had lost their limbs; thousands and thousands had their ears, their noses, their fingers and their sexual organs ripped off by the frost. Many had lost their hair… Many had lost their eyelids. Singed by the cold, the eyelid drops off like a piece of dead skin… Their future was only lunacy."
- Andrew Roberts, Daily Telegraph, 25 July 2009.