A man who needs to catch a flight to Brazil with his gf, shenanigans ensue

I am trying to recall a movie title and my google searches aren’t producing much useful.

So I have the following criteria:

1. The opening theme song is “Give me Just a Little More Time” by the Chairmen of the Board (and it is their version). The graphics involve a small cartoon man hanging off a clock, jumping between the hands, stuff like that.

2. The movie came out prior to 2003. The Internet was not a thing here, nor were cell phones common. I’d even place the date earlier. Early 90s?

3. The plot: a guy who works at an airline ticket counter is at his last day at work. He has a flight to Brazil to catch that very night. He is going to embark on this trip with a woman he has been seeing who is married/involved with a guy who is Bad News. A subplot is a radio show where they call you up, and ask you questions about a maze (you answer “left” and “right” to a sequence of questions) and you get money if you win. One particular scene is this man gets the right answers and can’t give his name because he is hiding out in the woman’s (or someone’s) house. After several misadventures he ends up on a flight, by himself, but instead of Brazil the flight is going to Lebanon. (When this movie was made it was still in a low-level war I guess?)

I know this is odd but it’s been bugging me for a while now.

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