I think you may be half right. Calling it a grease hole is misleading. It was a tallow hole, and often called a “ tallor hole” by the mountain folk. Grease could have been used in it in the winter, in the southern regions where this feature is common, but not in the summer. So the most likely material to be found in such a hole, would be some sort of hard tallow combined with just enough bear, or venison tallow to allow it to transfer to a patch with just a little rubbing. I think the consistency of this tallow mixture would be similar to that of a modern cheap shoe polish.
It is surprising how many old Southern mountain rifles found their way to the West Coast. Over the years I probably have seen seven,or eight, of them here in Northern California.
Most show signs of rodent activity around the tallow hole, a sure fire sign that some sort of tallow once resided there. Two showed signs of either being chard on the inside of the hole, with a hot iron, or burnished to near ignition with a hardwood dowel. Those are the only two I have ever seen with this feature.
Hungry Horse