I don't know about the stain, but on my
custom JEM swirl neck and on my aftermarket birdseye strat neck I used Tung Oil that I bought at Home Depot. I believe the brand was Formby's. As far as the stain, that being an oil based product, will probably inhibit the oil from soaking in some. That would probably just mean less coats of Tung Oil.
It is simple to apply. Just take an old tee shirt or similar lint free soft fabric and apply a coat. Let it soak for about 20 minutes I think is what time was, and then buff with a clean part of that cloth. Then recoat and repeat. Then let set for 24 hours. I put two coats on my necks and I think that would be a minimum to protect from moisture.
Good luck.