Tennessee Williams wrote the play "Suddenly Last Summer."  The Motels
had a hit 1983 song of the same name.  Was the song in any way
inspired by or linked to the play (or the movie with Elizabeth
Taylor)?

This is an interesting question. I've found a multiple-choice quiz in
a cached page from the Rhino Records site which indicates that the
song is based upon the Tennessee Williams play:

"Suddenly Last Summer" by The Motels is based on the play of the same
name by....
 David Mamet  
 Truman Capote  
 Tennessee Williams  
 Brendan Behan  
 Samuel Beckett 

http://216.239.33.100/search?q=cache:8saTqOhYthsC:www.rhino.com/RMAT98/jpage2.htm

(Note: The page linked above did not display properly for me. If you
cannot see the text, try scrolling down the page while holding down
your left mouse button, as if you were going to cut and paste.)

Unfortunately, I was unable to locate any other references on this.

I had also seen that quiz, which led me to believe there might be a
connection, but I need more direct evidence.  Thanks for your efforts.