The only times I have ever used the External trigger input on a scope was when I need to see the timing of two signals with respect to a third signal. And that was for square waves in a digital circuit, so I only needed to know where the edges were. One big problem that I see with trying to use the Ext input to measure phase of something like a sine wave, is that you can't actually see the waveform, which makes it difficult to know where to make your timing reference from.
Why do want to use the External input instead of the two regular channels?