I assume the special reversing module has it's own built-in logic so it "knows" all of the conditions and doesn't do something "bad"?
If you have multiple engines and you just want to reverse one section of track, the track sections need to have their own relays do they can be controlled separately.
If a short doesn't kill/damage the power supply, you can simply monitor for an "unusual" drop in voltage when there's a short.
...Otherwise you're essentially measuring resistance... Generally, a DMM measures resistance by supplying a (small) known current and measuring voltage (then "calculating" resistance with Ohm's Law).
It's easy if there's no voltage (other than the what your "meter" is supplying) and no train, because all you need is a power supply through a (series) current limiting resistor. You'll get full-voltage with an open circuit and no voltage with a short.
A couple of things make it difficult...
If there's a train you have to measure the difference between low resistance (the train motor) and very-low resistance (a short).
If there's voltage applied, you'd have to measure current (and the voltage). i.e. You can't use your DMM to measure resistance when the circuit-under-test is powered-up.
Making a constant current source isn't "easy".
Measuring current isn't "easy". There are current-measuring modules (Hall effect devices), or you can try to measure a (small) voltage drop across a small resistance.
The Arduino can only measure positive voltages and it measures relative to the Arduino ground. That makes it tricky to measure reversed voltage, and it means any "current-measuring" resistor has to be on the ground-side of the power supply.