Gilsonite - true Gilsonite, mined in Utah I believe - makes for a wonderful "asphaltum" that is not only hard and non-sticky, but also is relatively transparent which also is a true characteristic of genuine historical asphaltums. In fact, painters historically used light varnishes (i.e., thinned) tinted with hard and transparent asphaltums to add a bit of an 'aged' tint However, Gilsonite would not have been used historically as a varnish ingredient in this country until the very late 19th century, when it was discovered.
The problem with describing a finish as involving "linseed oil" and "asphaltum" is that it is essentially like writing up a recipe for a meal and noting that the primary ingredients are 'meat' and 'vegetable.' Come again? Hardware store linseed oil is garbage - we all know that. Of course there are better variants available if you purchase from an art supply, or you can make your own which will be much more true to the oil the early gunsmiths would have known. There are variations to be found in the linseed oil that was available in the 18th century, and as I noted previously, the term "asphaltum" was used to refer to a wide variety of bituminous products. Some were suitable for a wood finish or varnish subject to frequent handling and some were not. So my bottom line is this: be specific.
I distinctly remember someone a number of years ago at one point mentioning - somewhere - pine tar. I believe it was Wallace in a video, or perhaps in person, but if not then I apologize for attributing it to him. Sometimes in more recent years (20th century), this has also been referred to as asphaltum. It is not, very definitely not. Furthermore, it never would have been referred to as asphaltum in any historical context. Also, if someone can render a truly hard and non H2O permeable finish using pine tar, I have a bridge in Brooklyn available for sale. Good for horse hooves, though.