It is mentioned at least twice in the What's My Line writeup for episode 846 (1/22/67) that Herb Alpert's first recorded vocals for the TJB were in the song "This Guy's in Love With You" from 1968.
However, there are at least two instances where Herb Alpert's vocal appeared on a Tijuana Brass song prior to "This Guy's in Love With You" -- both of these instances were also prior to Herb's 1/22/67 appearance on What's My Line. Herb did say on the show that he was not a vocalist, but that was not 100% true at the time (it was about 99% true).
The first vocal instance I am aware of is the song "Hello Dolly!" on the "South of the Border" album from 1964.
The second vocal instance was in the song "Mame" which was a top 20 single in late 1966 (just before this show was broadcast, in fact). "Mame" also appears on a TJB album from this time -- I think (but am not sure) it was on the "What Now My Love" album.
Both of these vocals are not first class -- one might deem them throwaways and each might have been done in one take -- but he does sing a complete verse in each song, and thus should be considered vocals.
This show from 1/22/67 was recently rerun on GSN on or about February 1, 2008 -- I saw it that day for the first time (although I know it has been shown on GSN several times in the past) and afterwards looked at the writeup and first saw this discrepency. Hence my piping up about it now.