  Let $F$ be a totally real field and $K$ a finite abelian CM extension of $F$.
Using class field theory, we show that our previous result giving a strong form
of the Brumer-Stark conjecture implies the minus part of the equivariant
Tamagawa number conjecture for the Tate motive associated to $K/F$. We work
integrally over $\mathbf{Z}$, in particular the prime 2 is not inverted. This
note can be viewed as our perspective on the recent work of Bullach, Burns,
Daoud, and Seo. Following their philosophy, we show that the functorial
properties (i.e. norm compatibilities) connecting the strong Brumer-Stark
conjecture for varying number fields actually implies the minus part of the
equivariant Tamagawa number conjecture.
