Brushed DC motor chassis connected to each terminal
It's not a fault.  This is normal coil to chassis DCR.

The motor power and current rating I(rated)=Pm/V or Ravg=V²/Pm at max power. Thus Ravg=12*12/50=2.88 Ohms Although most DC motors have a DCR as low as 10% of the average effective resistance, these must be designed for low surge current or ~3x I rated max at 50W and 14.2V.

You measured 1.2 Ohms DCR so the surge or starting current will be Is=V+/1.2

Since the MOSFET switch shares the same current, it must be much lower than the motor DCR to avoid excessive heatsink costs, typically Rdson &lt; 10% DCR or in thus case &lt; 3% rated effective motor impedance or 10mohm to 120mohm with a strong preference towards the former.

So let's estimate the required Rdson. You do the math on Ploss and Rja thermal loss ['C/W]

The encoder may be useful or  important to detect load velocity in case of stall