What would be the best way to get rid of this smoke-stain left by the previous owner, who it seems left burning cigarettes in the left ash-tray, and the smoke just steadily trailed up and over the years this happened.

(taking a picture now, will upload in ~5 minutes)

http://img17.imageshack.us/img17/2283/0528091320e.jpg
http://img17.imageshack.us/img17/512/0528091320a.jpg
http://img17.imageshack.us/img17/6955/0528091320b.jpg

I'd try rubbing or denatured alcohol. But be careful...there is a chance either (the denatured alcohol more so) could take the color up along with the smoke stains.

Tried it with some 91% isopropyl that I already had under the sink, but it didn't work at all. =\

Try some regular GoJo hand cleaner. A few years back, a friend had his 1967 Olds 442 Dash pad resurface. The place that did it recommended actually using GoJo to clean and protect the vinyl. Since then, I've used GoJo (or equivalent) to clean up factory carpeting and just about anything else of really tough stains..........even pulled windshield sealant "spilled" from a replacement job from the carpeting that the shop was careless about. Good luck.

I would think the reason why GoJo works as well as it does is that it contains lanolin, actually any of the lanolin based hand cleaners should work just as well. Lanolin is a wonderful cleaner and works well on

Pressure sensitive label adhesive (after the label itself was removed)
Gasket sealer
Road asphalt and tar
Latex house paint
Splattered bugs
Dried but not cured spray can enamel

You would need to use a brush with some of these but the stuff works wonders, it would definitely worth a shot.