As an organization, the JBS does not officially make political endorsements but over the years, JBS officials have given their members credit for the election of people whom they regarded as reliable conservative anti-communists. For example, Robert Welch boasted that JBS members helped elect Ronald Reagan as Governor of California. In 1968, the candidacy of Alabama Gov. George Wallace for President was largely an operation of JBS members and supporters.
The problem with your question is that members of organizations can devote their energies to promoting ideas and electing specific candidates without any "official" endorsement by their organization. Robert Welch, the founder of the JBS, made no secret of his support of Sen. Barry Goldwater in 1964.
The JBS is organized as a "monolithic body" -- with direction from the top. It does not take votes of its members to determine its policies or leaders. But every available measurement of the sentiments of its members and its leaders makes its preferences regarding political candidates unmistakable.
For example, the JBS publishes what it calls a "Freedom Index" (previously known as Conservative Index) to measure the degree to which U.S. Senators and Representatives adhere to Constitutional principles (from the Birch Society's perspective). Very few politicians ever score 100% according to the JBS. Among those who have done so are Rep. Ron Paul of Texas and former Sen. Jesse Helms of NC.