Popular Science, June 1940
Applying WD40 will also do, being 'oil' yet with a very varied mixture of weights. The lighter fractions may help with the moistening throughout. After the spraying technique with WD40, it does however take some time for it all to even out.
So replicating this sound advice as given in the pages of Popular Science...
Pressing the blotting card gently onto the ribbon (or clip) and winding the ribbon back and forth a couple of times works to even the oil out. There's just that little bit of a shine on the ribbon after the oiling. Probably the oil is still mostly on the outsides of the ribbon and will need some time to fully moisten and release the dried-up ink.