Electrical resistance sensing could work but perhaps not directly into the Arduino. You may need a simple circuit to give the Arduino pins something it can work with.
Get two probes, one tarred up in a way you’d like to avoid and one that’s only been in clean gas. Separate from the Arduino, get the resistance measurements you want with a multi-meter. Then figure out how to replicate the multi-meter reading with a simple circuit that can feed an Arduino pin as a second step.
Different idea… what about spectroscopy? I see research papers characterizing coal and petroleum tars by their color spectrum. You won’t need fancy scientific instrument. LEDs and/or simple optics can read a color “fingerprint” of tars. It would be non-contact which is a huge plus.
Sparkfun even has a spectroscopy demo board that connects to Arduino with a software library
It does a wide range of light frequencies - wider than you probably need. The scientific literature I found on tar spectrums focused on only on infrared. Actually you might get away with a few carefully chosen IR LEDs and some phototransistor sensors for ~$5 tops. Message me if this is a direction you’d like to go. I have some background here that could be useful.