The Dell Optiplex 760 that I’m using as a rendering box has an internal “business audio” speaker that is not disabled by plugging an external speaker / earphone into either the front or rear audio output jack. The tiny volume control applet in the Xubuntu 12.04 notifications panel doesn’t provide any control over the sound card; it’s definitely not a mixer and its Sound Settings button calls up the Pulseaudio configuration which is oddly unhelpful.
xfce4-mixer, add it to the panel, fire it up, select the
HDA Intel “sound card”, enable all the controls, slide rightward until
Mono appears, click the speaker button under the slider to mute it, and you’re done.
Memo to Self: there ought to be a BIOS setting for that.