Okay, I've essentially re-drawn on my own board what you provided previously, but I'm just covering my bases here.
Here's my proposed setup:
If I hold the board to the light, I can see the red lead headed to the bottom right pin in the photo above, so this should tell me (even w/o a multimeter, which I've tested as well), that this is my "high" and therefore, my solder point for the NPN collector.
One of the other pins that doesn't read out any volts is going to be my low (ground), and the NPN Emitter gets soldered to it.
NPN base is getting connected to one of the Arduino I/O's with a resistor between.
All good so far, right (hopefully)?
Under such a setup, I'm not using the Arduino itself to supply any power (I think where some of my initial confusion came from between us), and as such, the 9V battery remains in my setup to supply the needed power. Correct?