On November 1, the Texas Democratic Party filed a lawsuit against the Texas law on order of candidates on the ballot. Texas Democratic Party v Hughs, w.d., 1:19cv-1071. It is assigned to U.S. District Court Judge Lee Yeakel, a Bush Jr. appointee. Here is the Complaint.
The Texas law says that the top names on the general election ballot are the nominees of the party that won the last gubernatorial election. Thus Republicans have been listed first for over 24 years.
The Complaint has the same footnote as in the Arizona Democratic Party lawsuit on the same issue. It says that if the party wins the lawsuit, the relief should not apply to minor parties or independent candidates, and quotes Timmons v Twin Cities Area New Party.