For the 2465 set the vertical mode to Alt and the trigger source to Vert.
Then whenever the Alt is sweeping channel 1, the trigger uses the channel 1 signal. And when sweeping channel 2, the timebase triggers using the channel 2 signal. Most of the later (>= 1968) Tek analog scopes have a Vert (or equivalent) trigger source selection.
Dave, that points to the reason why DSOs do not usually call it "alternate triggering" and why it ever existed in the first place. It also explains what the vertical source is.
The earliest oscilloscopes took their internal trigger signal from the vertical deflection plates. When switchable internal trigger sources were added, this became the vertical source. But when this is done on an oscilloscope which supports alternate switching to display more than one channel, it becomes alternate triggering for essentially free. Chop mode did not work with this configuration because the trigger would see the chop signal at the vertical deflection plates and trigger off of that instead.
To support higher bandwidths, later oscilloscopes included a separate electronic channel switch for the trigger source which usually did not include the vertical deflection plates as a source. To preserve the vertical source selection, the channel switch was driven from the alternate signal when the vertical source was selected and you can find this configuration on oscilloscopes into the 1990s. The big advantage of this configuration, besides higher bandwidth, is that chop mode can now be combined with the vertical trigger source in a useful way by adding the two channels together to produce the trigger signal. Surprisingly, this actually works in many cases.
So that is why and how many analog oscilloscopes had a vertical or VERT trigger source which allowed alternate triggering. Early DSOs which copied the architecture of analog oscilloscopes with analog channel switches also often include this as an explicit feature.
Where alternate triggering is really useful is displaying separate waveforms which have no coherent relationship without a second or more expensive oscilloscope. The switching waveforms from a power supply that has a separate power factor correction circuit is a modern example of this.