Tim saying “Honestly, I hope that John learned something from her” (“her” in reference to Gertrude) is crushing in the context I think he means that in.

Tim wouldn’t be happy if Jon took notes from Gertrude’s playbook. We see that in The Unknowing when Tim gets upset that Jon and the rest of the crew want to focus on blowing up the building instead of trying to save the dancers who have already been skinned, which is exactly what Gertrude would have done if she were in the situation.

So Tim doesn’t actually want a Gertrude version of Jon. He doesn’t actually want him to put stopping the fears over having humanity for the people around him.

Except in one case. He does want Jon to be strong as Gertrude when it comes to sacrificing one person.

And that’s himself.

He wants Jon to have the strength to use him to pull the trigger because he’s done, and needs Jon to have a strong resolve in order to see that through. That’s what his speech really boils down to. Tim is saying that he wants Jon to be cold enough to sacrifice him. Not the dancers who were innocent people caught in a nightmare, and not the humanity that went with them.