OK, I run Fords, so I don't know the answers from experience. But, since no one else has figured it out, I decided to jump in.
You would expect a code 13 if you unplugged the O2 sensor, but you might not get it.
Certain other conditions have to be met before the ECM will think there is a problem.
That sensor does nothing until it reaches 600 degrees, so the ECM does not expect anything at first.
It puts about 450mv on that line, and then measures it. Since the sensor is supposed to be open until it starts working, the ECM should see 450mv whether its hooked up or not.
So, no code.
If the line were shorted, then it would see 0 volts, and might set a code.
Then, it waits. If other conditions are met, and there is still no action, it then will set the code.
I did not know all the necessary conditions, but I have looked them up. Here is a listing......
Trouble Code 13 indicates that the exhaust stream oxygen-content sensor (O2 sensor) is not responding as expected. When cold, the sensor is 'biased' by the ECM to about 450 millivolts. Before it warms to at least 600 deg F (315 deg C) it acts as an open circuit and when the ECM reads it, it reads the 450 mV bias. The ECM expects the sensor to warm in a short period of time and begin sending its own voltages. The general conditions for this code getting set are:
- engine running at least 2 minutes
- coolant temperature at least 50 deg C (122 deg F)
- O2 voltage not fluctuating (i.e steady between 350 and 550 mV)
- TPS signal above idle
- all above conditions met for 60 seconds
Typical causes may include:
1) Defective or degraded O2 sensor
2) Deposit-contaminated O2 sensor (running leaded fuel, RTV silicone deposits etc)
3) Corroded/defective O2 sensor connection
4) Defective sensor ground circuit
5) Defective connection at ECM
6) Defective ECM
NOTE: If codes 21 and/or 22 are also present cause '4' above should be checked first.
So, in theory, if you leave it unplugged, let the engine run until its warmed up, then run it above fast idle for at least a minute, it should throw a code 13.
As for the code 51, that is only if it fails a certain internal check. If that part checks good, you should not see that.
Be sure to check all grounds you can find. Take them loose, clean things up and replace them.
Don't forget any around the battery or the ECM.