I don't know why it was showing a sine wave either. But, I did some poking around. For some reason, on the AY-AT board (or mine at least), the negative terminal on the battery connector is NOT a good place to put the ground for the scope. I think the DC connector has some sort of disconnect when something is plugged into it? Makes sense, perhaps, so that you aren't powering it both from an external DC supply AND a battery at the same time. 9V + 9V = bad.
Once I figured out how to use the trigger function, I was able to get valid readings. See attached. What you are seeing in terms of the change in voltage is when I touch the probe to the NPN. This is after the AY-AT is already on (I can tell by the red LED).
I'm truly sorry for my n00bness, but I do appreciate all the help!
What I'm guessing you need, however, is a trigger NPN at the time that the decoder is pressed. Is that correct? If so, that is proving difficult to accomplish logistically as I have to manually hold the probe in place on the bottom of the board. How does one set up the probes to that they stay in place while an external, manual, mechanical trigger is applied? I have nothing for the alligator clip and probe grabber to clip on to. Should I attach something to the solder joints temporarily for testing purposes?