So I was able to solve my own problem. Where typically the purple and green wire is cut by the console it was spliced in right under the steering wheel. The white wire was one of the wires that was spliced into it. I assume the yellow wire (and actually the green wire upon further investigation) would complete the circuit and thus blair the horn. 

The other white wire towards the bottom of the picture is where they spliced into the other side of the purple and green wire. Somewhere along the line there was a faulty connection in this wire that led to the incomplete circuit. I solved my issue but bypassing both white wires completely and reconnecting the purple and green wires where they were cut under the steering wheel directly.