Where does this connect to.... PICS!

Kurt is right. The broken piece goes to the oil level sending unit, which is a PITA to get out and usually breaks. The other side plugs in on the driver's side and is held close to the oil pan gasket next to the motor mount. The other plug is for the O2 Sensor.
 
That harness plugs in just below the oil pressure sending unit. The harness from the fuel injectors on the drivers side goes down by the distributor and by the oil pressure sending unit where the o2 harness connects to it and runs to the o2 snesors.

I know that plug very well because I accidently left it unplugged when I first fired my new engine.