"Have a Big Time in Texas” is a Texas tourist slogan that was advertised since May 1985. Texas is a big state, so people can have a “big time.” In 1987, “Another Big Times in Texas” was used as a tourist slogan.
19 May 1985, The Times-Picayune (New Orleans, LA), pg. C-23, col. 1 ad:
HAVE A BIG TIME IN TEXAS.
OCLC WorldCat record
Texas sesquicentennial guide to events, 1986.
Author: Texas 1986 Sesquicentennial Commission.
Publisher: [Austin, Tex.] : Sesquicentennial Commission, [1986?]
Edition/Format: Book : State or province government publication : English
Cover title: Texas, official 1986 sesquicentennial guidebook : have a big time in Texas.
9 February 1986, Victoria (TX) Advocate, “Texan makes anti-litter notes,” Texas Weekly Magazine, pg. 2, col. 1:
Kershaw also is responsible for the Texas Tourist Agency’s 1986 national TV and radio campaign, “Have A Big Time In Texas.” He composed and produced two pieces for the campaign, one a “hot,” slick piece reminiscent of Miami Vice, with quick cuts and synthesizer.
29 November 1986, Dallas (TX) Morning News, “A big-time budget for tourism”:
The advertising campaign for 1987 will use the slogan, “Another Big Time in Texas,’ following this year’s “Have a Big Time in Texas.’
January 1987, Texas Monthly, pg. 63, col. 1:
Visitors learn that one can, indeed, “Have a Big Time in Texas.” That is the slogan TTDA used to promote tourism in 1986. The new slogan follows logically: “Another Big Time in Texas.”