You did not try hard enough.
You have the wrist singularity when a4 and a6 are parallel.
Do a inverse kinematics and you will find that point.
I think that every robot manufacturer keeps his strategy secret.
Yeah my last resort is to check multiple points on a path if their a4 and a6 are parallel. Assuming only one singularity point exists in a path, it becomes a finding local maxima problem. Just wondering if there is a better solution.