I purchased a second hand PH-3 from ebay a few months back, so far i love the sound it makes. I'm curious about the expression pedal input. As you can see it has a second input:

My PH-3 didn't come boxed, so there was no manual included. So far i've been able to figure out that this thing is what plugs into the second input.

I haven't been able to find a single video on youtube demoing the two being used together. Does anyone own one of these, along with an expression pedal... and can explain to me what it sounds like? (or link to a sound/video if you could!)

I dont have that pedal but I do have pedals with expression inputs. I have the hot hand 3 from source audio verses the standard expression pedal like the one you linked. The pedal will modulate the sound coming into the pedal. Just youtube expression pedal and you will find examples of how the expression pedal changes the sound.
Yeh, i've had a look at some random pedals used with the expression pedal, can't seem to find anything close to a phaser though. It's hard to assume what it might sound like.

I'm more curious about what it would modulate with the PH-3. I guess it would modulate either the depth, or the tempo? Is there a universal way that it modulates the sound, or does it depend on the pedal itself (PH-3 is a digital effect).
I would assume the depth but just go buy one they are only like fourty bucks new and if you dont like it return it. Or if a store has a floor model out ask to run some pedals with it most places will not care .