Don't know of this will work, but soaking the nut and saddle in a strong cup of cold tea, for a day or two, may produce the stain you are looking for, maybe worth a try, as cheaper than buying a new tin of stainer. 😀
WAIT???!!! I don't have time to stinking WAIT!!!
I emailed Bob Colosi, the famous nut, saddle & pin seller. I asked if wood stain was OK. He said no problem, they experimented with it, but they use their own home brew stain that he wouldn't divulge.
But looking at the MinWax stains available, Golden Oak looks to be about the same as a few other light colored stains. I don't think I can find a lighter stain, other than maybe diluting this one. It's many decades old, it could be a bit concentrated.