This is what Ceolas Fiddle Tunes site has to say about it:

SENECA SQUARE DANCE. AKA and see "Georgia Boys," "Got a Little Home to Go To," "Higher Up the Monkey Climbs," "John Hoban's Polka," "Running from the Ferderals," "Waiting for the Federals." Old-Time, Breakdown. USA; Arkansas, Missouri. G Major. Standard. AB (Johnson): ABB (Ford): AABB (Phillips, Songer). Johnson (1982/1988) notes that there is an old hymn set to this tune, but does not give specifics. The melody is known to Irish musicians as "John Hoban's Polka" and appears to be related to the tune "(What Shall We Do with a) Drunken Sailor" and perhaps the gospel song "Rock-a My Soul (in the Bosom of Abraham)." "Seneca Square Dance" appeared on the Challange label (a subsidiary of Sears and Roebuck) on a 78 RPM recording by one 'Fiddlin' Sam Long of the Ozarks' (1876-1931, who actually was from Oklahoma but won a big contest in Missouri, according to Charles Wolfe) and was reissued by County on an LP entitled "Echoes of the Ozarks" in the 1970's. Long recorded the tune via acoustic, not electronic methods in 1926, and despite the rather poor quality of the sound it sold well in the Mid-west and West. Gus Meade and W.L. McNeil researched Long and discovered he had been born in 1876 and died sometime in March 1931 (perhaps in Wichita, Kansas). He was the first Ozark fiddler to have been recorded.
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"Seneca Squaredance" has been, and continues to be, a popular tune among regional fiddlers. Fiddlin' Bob Larkin recorded a version with words called "The Higher Up the Monkey Climbs." Alton Jones of Theodosia calls it "Seneca War Dance" and Cliff Bryan of West Plains calls it "Got No Little Home to Go to." It is infrequently called "Echoes of the Ozarks," the name of a different tune (by Clyde Davenport, for one).
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The melody was featured in the score by Ry Cooder for the film The Long Riders. It seems that one of Cooder's associates, David Lindley, previously performed an ideosyncratic version when he played with folk-rock musician Jackson Browne. There was no name attached to it and it was called "David's Fiddle Tune" at the time.
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The origin of the title is obscure. Jim Kimball, a musicologist from Genesco, NY, points out that many Seneca indians (part of the Iroquois nation) were relocated to Oklahoma after the War of 1812, and that there is still a large community of Seneca in the northeastern part of the state, not far from southwest Missouri. The tune may also be called after the town of Seneca, Missouri, in the southwestern part of the state (which may itself have taken its name from the Indian tribe). A distanced, somewhat odd although regularly phrased version appears in Pioneer Western Folk Tunes (1948) by champion Arizona fiddler Viola "Mom" Ruth, under the title "Get Away from the Federals" with "Fall of Paris" given as an alternate title. Source for notated version: John Hartford [Phillips]. Ford (Traditional Music in America), 1940; pg. 122. Johnson (The Kitchen Musician: Occasional Collection of Old-Timey Fiddle Tunes for Hammer Dulcimer, Fiddle, etc.), No. 2, 1982/1988; pg. 12. Phillips (Traditional American Fiddle Tunes), Vol. 2, 1995; pg. 125. Songer (Portland Collection), 1997; pg. 179. Recorded by Ozark fiddler Sam Long for Gennett Records c. 1928. Revonah RS-932, The West Orrtanna String Band - "An Orrtanna Home Companion" (1978). Kerry Elkin et al - "Tradition Today."
T:Seneca Square Dance
L:1/8
M:C
S:Jay Ungar
K:G
D/D/D G|{A}B2 B>A d B2 A/G/|{A}B2 B>B A G2 E/D/|{A}B2 B>A d B2 A/G/|
A/B/A/G/ EF G:|
|:Bd|[B2g2] g>g d B3|[B2g2] g>a b e3|g/a/b/a/ ge d2 B/A/G|A/B/A/G/ EF G2:|

WAITING FOR THE FEDERALS. AKA and see "Running from the Federals," "Seneca Squaredance." Old-Time, Breakdown. G Major. Standard. AA'BB'. Bain (50 Fiddle Solos), 1989; pg. 22. WHR 01, Aly Bain - "First Album" (learned either from fiddler Jay Ungar or singer/songwriter Jim Ringer, Ungar's source. Ringer would sing or play on the harmonica the melodies of fiddle tunes he had learned when growing up in Arkansas).
T:Waiting for the Federals
T:Seneca Square Dance
L:1/8
M:C|
K:G
B4 B2AB|d2B2 BAG2|B4 d3B|ABAG E2D2|
B4 B2AB|d2B2 BAG2|ABAG E2F2|1 G3A G2DG:|2 G3A G2Bd||
|:g4 gage|d2B2 BAG2|g4 gfga|b(ee)f e3f|gaba g2 ge|dged BAG2|
ABAG E2F2|1 G3A G2Bd:|2 G4G4||