Steve,

Yes, the type of alcohol is important; but I can't tell you what to use. I know that rubbing alcohol is more likely to be a 70/30 mix of isopropanol (IPA) and water than it is pure IPA. Surely the 70% stuff won't mix with linseed oil. Likewise, neither pure methanol nor denatured alcohol (ethanol made toxic with methanol or other additives) will mix with linseed oil. Possibly 99% pure isopropanol is soluble in linseed oil; don't know, don't have any on hand. But, if you're going to go looking for an "alcohol" to use, search for pure IPA.