No, not that one.
In the first verse, Simon sings:
You walked into the party
Like you were walking on a yacht
Your hat strategically dipped below one eye
Your scarf, it was apricot
You had one eye on the mirror
And watched yourself Gavotte
Who the heck was doing the Gavotte in the late 60’s/early 70’s? Was this a thing amongst the upper crust? Also, what does one look like entering a room “Like they were walking onto a yacht”? Unsteady?
Swaggering I think. A manly, swaggering, forceful walk.
Gavotte for the rhyme, I would imagine. She just meant dance.
I always pictured a preening sort of dance…
Well, look, so long as you’re already picturing Mick Jagger…
I’m thinking “yacht” tells us in fewer syllables about the sort of party she is imagining and the sort of people there. “Penthouse” could have done the same thing but it’s harder to rhyme than “yacht” 
You might have that backwards: imagine (a) the story is true, and (b) the guy simply was wearing an apricot scarf; what happens when she casts about for a rhyme?
It’s a metaphor.
She was widely criticized for the rhymes in that one at the time, IIRC.
I thought it was a pun.
It’s Vorshtein.
Anyway, thanks for clearing that up for me, OP! I forced it to say “As you watched yourself go by”. Of course I also thought it was:
Well I hear you went to Saratoga
And your horse, naturally, won
Then you flew your [winnings or women] up to Nova Scotia
To see the total eclipse of the sun
I should really get my ears examined.
It’s LearJet. As in he’s rich enough to have one at his disposal and doesn’t need to wait in line at the airport.
Same here. I had never heard the word “gavotte” before reading this thread.
And I have had my ears examined. The diagnosis was, I can’t hear for shit. (Hey kids! When you’re using power tools, don’t forget the ear protection!)
Without the “up.”
I always heard “go past,” until I listened to a digitalized recording of the song.
No, the word “up” is in there.
“Then you flew your LearJet up to Nova Scotia to see the total eclipse of the sun.”
Listen to it.
Huh! I’ve listened to it a million times, and I’ve never heard “up.” 
Fun thing was, I convinced my dad to fly us up to PEI to watch that very same eclipse. (club-owned Cessna 172, not a Learjet.) Quite a sight.
I hear it quite clearly. I’ve always heard it that way.
Well, that’s the way I’ve always heard it should be.
It’s a metapun.
Bravo. Nobody does it better.