Two days ago, on Tuesday, I posted a movie trivia question. The answer is Leaving Las Vegas.
Although the neon sign had no significance in the story itself, it was shown briefly, at least four times during the opening credits.
If you have seen the movie, you know that the opening credits start a little late. The sign in question was shown for the first time at 17 minutes 35 seconds on the DVD, for 8 seconds. It was shown in brief clips at least another three times in the following minute.