If they do decide to keep him then at the very least some reflection is in order, even before posting "I'm not sure about this one".
If our highly rated and experienced new Technical Director, with access to much more information about our problems than we have, thinks that we're better off keeping the manager than pivoting to a new one, then there's likely at least some merit to the decision. Perhaps he's aware of some things that you aren't, or there are some things you hold to be true that he is aware aren't. Perhaps he doesn't apportion blame for some situations the same way you do. If you're going to write it off as wrong before genuinely considering why it might be, that just boils down to zealotry.
It works the same the other way as well. If Wilcox decides to part ways with ETH, then his supporters will need to accept that there's likely some solid reasoning behind it, rather than a reactionary knee-jerk.