Potentiometer or momentary switch, how to better recognise what was connected?
If you know it is an active device, you test 1st with a DMM voltmeter.
Since you know this is passive, you start with a DMM Ohmmeter which is 10uA to 1mA CC and measure voltage.  An analog meter in Ohmmeter scale would be more responsive but less accurate.

How you implement this circuit is irrelevant unless you have tolerance specs for these options and may include 4) None of the above
Some audio drivers have this feature for Windows when enabled, that can auto-detect any audio port as having ;

a speaker connected, by Low impedance to gnd,
an electret microphone, by midscale DC voltage from external bias to V+
or open circuit, detecting V+

Using the same approach you can define 3 states;

A switch with a 9X resistor across it to get 90% of V+ when open and 10% V with 10% series R when the switch is closed.
A slider pot with 20% series R's on either side that controls the V+ bias confined output voltage range with the chosen standard pot value that does not conflict the voltage in states 1. or 3.   15% V+ &lt; Vx &lt; 85% V+
Open circuit V=V+ from external R bias.




simulate this circuit &ndash; Schematic created using CircuitLab
Something like this can detect the 3 states with voltage-current or by either sweeping with a DAC to detect a zero-crossing for the Voltage result or using an ADC to measure the voltage with V+ bias and series R.