Turns out, I had the wires plugged into the wrong sides of the diode (backwards). Doh! I switched them and now the car reads 14.37 volts at idle. Yay!
The new fusible link was replaced after the lights being left on and during diagnostics. I was just trying anything and everything at one point to figure it out.
The voltage would start at 12.6 (with a full battery charge) and just slowly drop a tenth every 30 seconds or so with the engine running, which is consistent with the alternator not knowing it should be charging while the diode was not connected correctly.
Thanks for the responses!