Where does my C wire go in this splice connection?
Based on the images and your comments, I would say that the wire splice you are holding in the first image with the thick brown and thin red wire would be where you want to connect your C wire.  Blue is the typical color to use, and I believe you have an unused blue wire going to your thermostat that will work (the cable with the unused blue and brown should be the thermostat wiring).

The thin red wire in that bundle and the thin white wire from that yellow/white splice go to the "cooling unit relay" from the schematic.  So the thin red would be the "common" side of the cooling relay and the white would get voltage from the thermostat.