Can we track what the secondary reviewer wrote, nudge them into action, or have them sign a review on behalf of the actual manager?

The secondary reviewer has just a helper role at this point, so what a secondary reviewer does can not be tracked, nor can they be nudged, nor can you distinguish their feedback from that of the main reviewer. It would be the official manager's job to collect feedback from the secondary reviewer.

An overview list of the secondary reviewers is available using the magic-column: