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in _tkinter.c, look for EventHook - you'll find the
EventHook function, which is called when the interpreter is
idle, and the Enable/Disable EventHook functions.

In readline.c, line 765, you'll find the call to
PyOS_InputHook, when waiting for input.

Perhaps a more general approach would be to let Python code
call PyOS_InputHook, for example, by defining
readline.call_input_hook() and readline.has_input_hook().
Then IDLE would be able to call them when idle, with no
Tkinter-specific code.