Wallace did campaign for an American Party candidate for Congress in 1969 in a Wallace-friendly district (TN-08 which went 48% Wallace, 28% Humphrey, 24% Nixon in 1968). It didn't turn out too well. From the original
Almanac of American Politics (1972), p. 772:
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EIGHTH DISTRICT Political Background
"Tennessee 8 comprises the northwest corner of the state. The district extends from the TVA lakes of the Tennessee and Cumberland rivers at the Kentucky state line to the city of Memphis. This area, physically and politically, resembles the Mississippi Delta country or eastern Arkansas: flat cotton lands, occasional small towns, and a population running about 24% black. The largest city in the district outside of the Memphis area is Dyersburg, with 14,000 residents. Most of the counties here are traditionally Democratic, but only those around the Tennessee River have given statewide Democratic candidates significant margins in recent years. Most of the rest of them responded favorably to the thinly-disguised segregationist appeals of Republican candidates like Sen. William Brock. The Shelby County (Memphis) portion of the 8th, like that of the 7th, is heavily white and very conservative.
"Perhaps because of its long-standing Democratic tradition, Tennessee Republicans did not strenuously contest congressional elections in the 8th for some time. From 1958 to 1969, the district was represented by conservative Democrat, Bob Everett, who faced Republican opposition only once during his tenure. In 1969, Everett died and a special election was called. George Wallace, who had carried the 8th with nearly 50% of the votes in 1968, came in to campaign for American party candidate William Davis, while Sen. Baker and other conservative Republicans stumped for the Republican, Leonard Dunavant. The race got some attention in the national press as a test of the Wallace and Nixon strategies in the South.
"The result made both look rather bad. Davis won 25%, Dunavant took 24%, and the winner, conservative Democrat Ed Jones, won 51% and an absolute majority, in the race. Jones, former commissioner of agriculture, had not asked outsiders to come in and campaign for him; he wisely relied on the traditional Democratic sentiments of the voters of his district. These people may plunk for Wallace in a presidential elec1tion and they may applaud some of the policies of the Nixon Administration, but most them preferred to stay with a Tennessee Democrat in what is, after all, a local election. Then too, against Wallace- and Nixon-backed candidates, Jones won the black vote with no effort at all. ..."
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See
https://www.ourcampaigns.com/RaceDetail.html?RaceID=373578 for the results of the election (and a map of the district as of 1969).
Jones
https://en.wikipedia.org/wiki/Ed_Jones_(U.S._politician) went on to be re-elected with few problems until he retired in 1988. Nixon's easy victory in the district in 1972 and Reagan's in 1984 didn't bother him at all. And that indeed was the problem with a third party in the South: people might vote for Wallace at the presidential level or for Nixon against McGovern in 1972 but why change your habit of voting for more-or-less conservative Democrats in congressional and other "local" elections? It was really only in 1994 that this habit was broken in much of the South.