Solved!!! Yep those are the correct connection points....when you're done there, call me, cause you're hired!OKAY! So I found the problem...
As it turns out, the problem was located at the light switch. While the white wire that feeds the outdoor outlet was connected, the black wire was capped off.
I'm not sure why this was done. Perhaps when the electric was redone in the kitchen, they didn't know what the wire was for and just capped it. Or maybe they intended to reconnect it and forgot.
So here is what we have in the picture:
1. The black and white pair in the 9 o'clock position are the power.
2. The pair at the 6 o'clock position feed the outdoor outlet (confirmed via continuity test).
3. The pair at the 3 o'clock position feed the outdoor light.
My connection plan is:
1. All whites tied together.
2. Black from the power will tied to the black going to the outlet. Off of this, a black jumper to one side of the switch and the black from the light tied to the other side of the switch.