I didn't realise that 'white spirit' was not recognised by that name in the US. I believe you call it 'mineral spirits' (a name not used in the UK!) or turpentine substitute.
Some cellulose paint thinners may work, but there are so many different blends and experimentation (and possible disappointment) should be allowed for.
I wasn't originally advocating any alcohol (potable or not), as water is a component and tends not to mix with or dissolve anything oily. However, iso-propyl alcohol (propanol; US rubbing alcohol), as used for switch/contact cleaning (and, usefully, leather stretching!) would possibly work on small spots, although not too easy to buy here.