Interesting potential new thread here. ''Etiquette in dealing with Celebs and Notable Personalities''
There are different approaches depending on the situation. (These days I'm no longer a gigging musician who gets star struck and has to stifle when meeting celebs. I'm in corporate event planning and entertainment contracting - allright it's a fancy terminology for AGENT (heheheh)..and I deal with celebs quite a bit. I treat them exactly the way I would treat anyone I like, but generally I don't bombard them with questions, and try and stay out their way and not invade their space. If they start talking to me and want to pursue a friendly conversation, then I just roll with it.
From a ''fan'' perspective, if you see someone you admire and feel compelled to go over and talk to them, make sure first of all they are alone or not engaged in a heavy conversation with whoever they might be with - so that you're not being rude and interupting them. If the coast is clear, by all means go for it. The sentence you mentioned about ''I just want to thank you for the pleasure your music (or whatever it is they have impressed you with) has given me over the years'' is perfect, and they'll respond positively and love it. They never get tired of these kinds of things.....but don't overstay your welcome. Move on and keep the buzz going for as long as you can.
I was working cruise ships years ago back and forth between Miami and Bahamas, and was sitting in the lobby of the Grand Hotel (don't know what it's called now - next door to the Paradise Island Resort and casino.) It was our day off, and my wife (also the singer) were in the lobby having a smoke and relaxing, and the lobby was literally empty. At that moment Jerry Lewis walked in all by himself. My wife is a huge fan and just bolted before I could get up out of the chair....so I stayed put and watched her go over and start talking to Jerry, from about 20 feet away. I couldn't hear everything they were saying, but then Jerry looked over and smiled at me and motioned me over.....He wanted to know all about us and what we were doing in the Bahamas, so we told him. Turns out he was there scouting locations for a movie (which later turned out to be ''The King of Comedy'' a classic in my opinion.) We talked for about 10 minutes and then he split.....We buzzed for the rest of the night and well into the next day, and of course got autographs.