DonM and others: I wanted a "momentary" function like that for Bass Inversion. For example, if most are plain chords and there is just one "on bass" chord in the whole song, I didn't want to be stuck playing all the chords in root position. Pushing the footswitch twice quickly to turn it "on" and "off" didn't always work. (Aside: hard to believe that NONE of the major brands have this as a momentary function!) So I did some research and solved it a different way...

There's a company called Midi Solutions that makes a module called a Footswitch Controller. You can program it to send one MIDI message on press, and a different one upon release. So, as long as vocal harmony on-off can be controlled with a MIDI message, you can buy the Midi Solutions module and obtain your preferred momentary control.

If you're really handy with electronics, you could probably build some kind of timer circuit with an arduino, raspberry pi, etc. The Midi Solutions module worked for me.