We generalize the property of Jacobi-orthogonality to indefinite scalar product spaces. We compare various principles and investigate relations between Osserman, Jacobi-dual, and Jacobi-orthogonal algebraic curvature tensors. We show that every quasi-Clifford tensor is Jacobi-orthogonal. We prove that a Jacobi-diagonalizable Jacobi-orthogonal tensor is Jacobi-dual whenever $\mathcal{J}_X$ has no null eigenvectors for all nonnull $X$. We show that any algebraic curvature tensor of dimension $3$ is Jacobi-orthogonal if and only if it is of constant sectional curvature. We prove that every $4$-dimensional Jacobi-diagonalizable algebraic curvature tensor is Jacobi-orthogonal if and only if it is Osserman.