White spirit is a petroleum fraction - less volatile than petrol, more than paraffin or diesel, so basically an aliphatic hydrocarbon oil. There are various alicyclic compounds found in white spirits, which contribute to the odour, low odour forms being the cleanest. White spirit has been implicated as a cumulative neurotoxin in "Chronic Painter's Syndrome".
Where these mineral oils are used, it is often possible to substitute them with a non-volatile vegetable oil. Instead of using best sunflower oil, I keep old chip oil. It cleans brushes like white spirit, diluting oil-based paint, and cleans paint off the skin much more gently, without the volatile elements that dry and irritate the skin in white spirit.
Rather than acting primarily as solvents, the hydrophobic oils coat the organic resins and plastics that make up the glue, preventing them from adhering together again, so in conjunction with an abrasive medium - it could be steel wool as in Brillo pads, or sharp sand, or even sugar crystals as a hand cleaner, the vegetable oil is effective in detaching from the substrate and removing adhesives, paints and bitumen.
Stainless steel pan scourers are more sturdy than steel wool, and do not leave particles behind that can rust and stain, and are less likely to produce puncture wounds than the steel wool can.
The final clean off can be done with washing up liquid and warm water, which is formulated to deal with organic oils in its stated uses.