What I think you may have is a mixture of pine tar mixed with what's called "tall oil" in English. Tall oil is a crude liquid type of resin (also called rosin or colophony). The mixture also probably contains a small percentage of turpentine (pine EO).
I've made pine tar soap from this kind of pine tar and tall oil blend. It will cause the batter to accelerate and heat up at least as quickly (or even faster) than pine tar, because resin/rosin reacts even faster and harder with lye than normal pine tar does.
So ... be aware that a volcano might be more likely. Not saying it will, just that it's more likely. Keep your ingredients on the cool side and be prepared to stir the batter with a spatula or whisk to control the batter if it starts to expand (volcano). If the batter does want to volcano, I'd instantly switch to a hot process method -- watch it like a hawk, keep stirring it to keep the expansion to a minimum, and let the soap cook in the pot until the chemical reaction settles down.
I don't remotely have a clue whether this mixture has any benefits for skin problems like "official" pine tar supposedly does. There's no scientific proof that official pine tar does anything for skin problems, and there's even less information about your pine tar oil. This is a mystery no one here can answer.
Tar can be made from many plant-based materials including pine, birch, juniper, coal, peat, etc. -- anything with enough resins to make it worth the trouble to make the tar.
Pine tar is the most common type of tar that people commonly have access to, but I know some people have mentioned birch and juniper tars -- I gather these are made in Scandinavian countries as specialty items. Peat is not very common in most parts of the world either, so peat tar will be another specialty product. Coal tar, which is still made, has fallen out of favor for personal care products so it is not as easy for small scale makers like us to find.
Tar is produced by pyrolysis, which is a method of heating carbon-based, resinous material in the absence of oxygen. Without oxygen, the carbon-based material does not burn; instead, it produces flammable gases similar to natural gas, the liquid resins drip out of the material and drain away, and the remaining solids that don't become gases or liquids are converted into charcoal.
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