What voltage for the battery do you want me to measure voltages at the nodes?

It's not easy to see the pin outs on that datasheet.

 

Here is the voltages from both battery voltages, is this what you mean by measuring voltage at each node?

 

Here is the voltages from both battery voltages, is this what you mean by measuring voltage at each node?

Yes, those are the voltages.

They don't make sense, however.
The output is OFF as it should be for a 11.5V battery voltage (1.21V due to feedthrough from R9).
But the 1.87V at the MOSFET gate indicates that it should be ON, not OFF.
Are you sure that 1.87V with respect to ground is correct?

Show the voltages when you increase the battery voltage above 12V.

 

Yes, those are the voltages.

They don't make sense, however.
The output is OFF as it should be for a 11.5V battery voltage (1.21V due to feedthrough from R9).
But the 1.87V at the MOSFET gate indicates that it should be ON, not OFF.
Are you sure that 1.87V with respect to ground is correct?

Show the voltages when you increase the battery voltage above 12V.

Yes the 1.87 volts at the mosfet is correct, I double checked it with my multi-meter and still 1.87 volts, here is the voltages for 12.08 volts for the battery. Honestly I'm puzzled too.

 

Try shorting the MOSFET gate to ground, which should raise the output voltage to the supply voltage.
If not, then you have a problem with the MOSFET or its pinout.

Also the values of R2, R3, or R9 seem to be wrong.
With a battery voltage of 12V, the voltage at pin 1 of TL431 should be ≈2.5V, not 2.38V.

 

A question was asked in this thread about the circuit under discussion and was moved to seed a new thread. You can visit that thread at this URL: https://forum.allaboutcircuits.com/...y-and-thermal-protection.142683/#post-1205948