Here's the honest answer. We can't tell you tallow treats eczema, and we'd be careful with any brand that does.
Eczema is a medical condition. Skincare isn't medicine.
What we can tell you is why it keeps coming up.
If you've been at this a while, you've probably tried both kinds of answer, and you already know the pattern. Something works for a fortnight. Then your skin is red, hot and angry again.
Skin that reacts is usually skin whose barrier is short of the fats it needs to hold water in and keep irritants out. Tallow is unusually close to what your skin already makes: the same fatty acids, oleic, stearic and palmitic, plus naturally-occurring cholesterol, which your barrier uses and plant oils don't contain at all.
That's the whole of it. It isn't treating anything. It's giving your skin back material it's short of, then sealing it in so it stays.
What people describe afterwards is consistent enough to be worth repeating. The feel changes first, often within a day or two, and that tight, prickly, stinging feeling settles.
Then over the first week or so the look catches up. Then the part nobody expects: the other products start coming off the shelf, one by one, until it's just the one jar.