The documentation suggests EditorApplication.pauseStateChanged as an alternative, but it does not provide the same functionality. The deprecated playModeStateChanged fires on entering play mode whereas pauseStateChanged does not.
EditorApplication.playmodeStateChanged = Old and deprecated
EditorApplication.playModeStateChanged = New and shiny
Please notice that “Mode” in “playMode” has different capitalization.
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Oh, duh. I don’t know how I missed that 
Thank you.