Frobenius forms on weakly primitive axial algebras of Jordan type

In a previous paper we studied ``weakly primitive axial algebras’’ with respect to more general fusion rules, for which at least one axis satisfies the fusion rules. In this continuation, a concise description is provided of the $2$-generated algebras we obtained in that paper and we show that in certain cases, the algebras have a Frobenius form, a key tool in their study.