Switch bool from False to True on key press?

I would like to let a boolean variable switch when I press a key on the keyboard.

For example, I write

activateE := Block[{}, edown = True;];
SetOptions[EvaluationNotebook[], NotebookEventActions -> {{"KeyDown", "e"} :> activateE}]

and then try to monitor the key presses via

edown = False;
Dynamic[edown]

While the key e now stops producing any text input into the notebook, unfortunately the Dynamic always keeps showing False, regardless how often I press the key e. What am I doing wrong, or how to do this properly?

EDIT:

Alternatively, I am trying the CurrentValue function. For example,

Dynamic[CurrentValue["ModifierKeys"]]

properly shows e.g. when the Ctrl key is being pressed. But if I try

Dynamic[CurrentValue["EventKey"]]

the output is None no matter which key I press. Is there an option of CurrentValue that would register a regular key press, like letter e?

EDIT2:

What seems to work, is

EventHandler[InputField[], {"KeyDown", "e"} :> activateE]

but only if I first click on the InputField to bring it into focus.

ClearAll[activateE]
activateE:=  Block[{}, edown = True;];
SetOptions[EvaluationNotebook[], 
 NotebookEventActions -> {{"KeyDown", "e"} :> activateE, PassEventsUp -> True}]

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