Or more specifically, the guitar intro? It’s also heard in the intro to the Ink Spots’ “We Three”.
Wasn’t this one used in a Warner Bros cartoon with a goofy turtle? That’s what I think of when I hear it.
Maybe the Minah (Mynah?) Bird music.
Arkansas Traveler is one that everyone has heard but may not know the title.
This one is a long shot, but could it be the opening part of Washington Square by The Village Stompers? That has a some what western sound.
I know this one too. It’s Mendelssohn’s “Hebrides Overture.”
I can totally hear the music you’re describing in my head. Could it possibly be some Hollywood studio stock music kinda like this?
That’s a major key, but all the clip clopping songs I can think of seem to be in major. I’m stumped.
Lots of “do-do’s” in this one, but it’s still too cheery and upbeat. Listen to the clip from Once Upon a Time in the West again and you’ll sense the same mood of my piece.
That clip reminds me of the instrumental version of the theme from the 1970 spaghetti western They Call Me Trinity.
The vocal version was used in the 2012 Tarantino picture Django Unchained.
It was composed by Franco Micalizzi, but IMO would fit in well with Morricone’s soundtracks, which I’ve always thought were the best parts of those spaghetti westerns by Sergio Leone. The “meatballs” if you will.
I know it’s not your song, because it’s not well enough known. But are we getting warm?
PS: Thanks for this thread, I’m enjoying it!
You’ve got the mood right.
Something clicked a few minutes ago while I was having a lie-down. I thought of honkey-tonks in old New Orleans, gamblers, the French Quarter, Bourbon Street.
I’ve done a search for tunes with Bourbon Street in the title but haven’t found any even remotely close. I think I’m on the right track, though.
(And no, it’s nothing to do with Kenny Rogers’ “The Gambler.”)
“The Old Fun City” from Butch Cassidy & tSK
Okay, I picked out the first part on a virtual keyboard. The notes are:
C3 F3 C4 C4 A#3 C4 F3 F3 / C3 F3 F3 C4 A#3 C4 / C3 F3 C4 C4 A#3 C4 F3 F3 / C3 F3 F3 G3 F3 E3 F3
The rhythm is:
4 1 2 3, 4 1 2 3. 4 1 2 three-and-a four! 4 1 2 3, 4 1 2 3. 4 1 2 three-and-a four!
This is the best I can do without formal training. I hope you can read it.
DING DING DING DING!!!
Yes, it is WASHINGTON SQUARE by THE STOMPERS!!!
THANK YOU! 
You get a lobster dinner at Scott’s the next time we’re both in London!!! 
(And thanks for “Arkansas Traveler” too. It’s another one I knew but couldn’t name.)
A song about a beatnik hangout in New York City, played New Orleans style. “Way out West” indeed!
Which also describes the final chorus of Paul Simon’s “That Was Your Mother.”
According to YouTube:
The Village Stompers “Washington Square” was the #1 Hit on the Adult Comporary Charts and reached # 2 on the Pop Charts in 1963. Washington Square Park is a landmark in the Greenwich Village area of New York City where the group got started.
Wow, 1963! I must have heard it dozens of times on my dad’s car radio when I was on summer vacation back in the '60s. I think it was the jazz part near the end that triggered my association with New Orleans.
Never underestimate the Power of Music!
Ironic, innit? 
Years ago that was one of the “tunes in my head” that I had to look up to get it out of my mind for a bit. I had heard it dozens of times but couldn’t remember the artist or title until it popped up on an oldies playlist one day.
Some great historical tidbits about Washington Square Park in that video.
Actually, the Village Stompers. And, yes, I know that song well. Would never associate it with the Old West, though.