iTerm2: Stopping the inactive pane from dimming
Found it! There is a setting in Settings -> Appearance -> Dim inactive split panes. I would have quite liked to be able to set it for just the two profiles, but it doesn't matter that much.
On newer versions of iTerm2 (Build 3.3.2+ for me), unchecking the following setting solved this:
Preferences(⌘,) -> Appearance -> Dimming
Then uncheck the first option:
"Dim inactive split panes"