Drying oils (linseed oil, tung oil, walnut oil, etc) can produce a beautiful finish. Simple oil finishes will have a very soft lustre that really shows off the beauty of the wood, and they can be waxed and buffed to a higher gloss. And a cured tung oil finish is more waterproof that some of the other options.
I've never used a pure oil finish on a pen because I've never believed that oil alone would be tough enough to withstand daily use. I have used a tung oil-based 'long-oil varnish' finish (made from tung oil and marine-grade spar varnish) on a few pens - it looks and feels very nice, but I'm still not sure about long term wear. I have used both pure tung oil, or a long-oil varnish, and then applied a lacquer-based friction polish topcoat. And I've used oils to enhance the wood color, and the applied WOP as a protective top coat with an interface application of a shellac-based sealer.
I've generally tended to prefer WOP on stoppers because it is hard enough to withstand banging around in a kitchen drawer, and is waterproof so the finished product can be rinsed off between uses.
However, I have made a few bottle stoppers with captive rings that I've finished with pure tung oil. When you are dealing with captive rings, the process of finishing gets complicated. You first have to sand and finish the ring after it has been rounded over and before it has been separated from the body of the turning. And later you have to finish the entire turning including the underside of the ring. A flnish like WOP is problematic because it can actually glue the ring to the body during that second stage of finishing unless you come up with some means to keep it separated from the rest of the stopper while the finish cures. Using pure tung oil gets around this process because all you have to do is apply the oil and then rub it in.