I know this doesn’t answer your question, but perhaps it’s a useful first step:
By the nature of the generalised eigenvalue problem you shouldn’t need to implement the involution term as you would for a time harmonic Maxwell problem where the frequency is not an eigenvalue of the system.
Consider the following. Let (u, \lambda > 0) solve the generealised eigenvalue problem, then we have
\begin{align} \nabla \times \nabla \times u &= \lambda u, \\ \nabla \cdot (\nabla \times \nabla \times u) &= \lambda \nabla \cdot u, \\ 0 &= \nabla \cdot u. \end{align}
If you modify your problem do you have a full diagonal and as such does the eigensolver converge?
Also there’s a very old (but excellent) demo here which may help.