Please help me understand this bjt set up works
I figured it out!! 

Pin 1 is VCC, connected to 12V in through a resistor that is also connected to the collector on the BJT. Input to NAND 1. 

Pin 2 is connected to the RC network, (which is a little strange to me and my next section to understand better) and is an input to NAND 1. 

Pin 3 is the output 0f NAND 1 and connects to pins 5&amp;6, the inputs of NAND 2. 

Pin 4 is the output of NAND 2, connected to a resistor/diode in parallel that go to pins 8 and 9. 

Pin 7 is ground, but in this circuit is connected to a capacitor in the RC network. 

Pins 8&amp;9 are inputs to NAND 3, connected to pin 4 through a resistor. I think the diode is extra protection from back EMF from switching. 

Pins 10 and 11 are outputs of NAND 3 and 4 but aren't used. 

Pins 12 and 13 are inputs to NAND 4, also connected to the base of the BJT AND inputs to pins 8&amp;9. 

Pin 14 is VCC. 

So: constant voltage to pin 1 of NAND 1 and RC on.off to pin 2 of NAND 1. Output feeds into NAND 2 which reverses the output (pin 4) and sends that to the BJT to turn it on/off. 

Logic is as follows. 

Pin 3=NOT(1 and 2)
Pin 4=NOT(5 and 6)
     =NOT(3)
     =NOT(NOT)(1 and 2)
     =(1 and 2)

And again, pin 4 is connected to the base of the BJT, thus turning it on and allowing current to flow from collector (that is connected to +12) to emitter (relay coil). 

Oh, my god I'm so relieved. This was causing me major anxiety and I had to put it down for a while to focus on other stuff at work. Finally came back to it about an hour ago and while I had the correct connections, I must not have been thinking about it correctly. Phew!