cursor color depending on insert or overwrite mode

how can I change the cursor color depending on insert or overwrite mode?

I looked at this page

https://www.emacswiki.org/emacs/ChangingCursorDynamically

and put as recommended 3 lines in the Emacs init file at the end of the custom-set-variables block as well at the end of the custom-set-faces block. In both cases the color of the cursor was black both in insert and overwrite mode.

This is my Emacs init file

(custom-set-variables
 ;; custom-set-variables was added by Custom.
 ;; If you edit it by hand, you could mess it up, so be careful.
 ;; Your init file should contain only one such instance.
 ;; If there is more than one, they won't work right.
 '(blink-cursor-mode nil) ; Cursor nicht blinken lassen
 '(inhibit-startup-screen t) ; Keinen startup screen für Emacs anzeigen
 '(x-stretch-cursor t) ; Cursor bei Tabulatoren breit machen
 '(show-trailing-whitespace t) ; Leerzeichen am Zeilenende anzeigen
 '(sentence-end-double-space nil) ; Keine zwei Leerzeichen nach einem Punkt
 '(require-final-newline (quote ask)) ; Zeilenende an letzter Zeile erzwingen
 '(column-number-mode t) ; Zeilennummer und Spalte in Statuszeile anzeigen
 '(show-paren-mode t) ; show matching parantheses
 '(transient-mark-mode t) ; show marked region (fails; work around see below)
 '(require 'cursor-chg)  ; Load the library
 '(toggle-cursor-type-when-idle 1) ; Turn on cursor change when Emacs is idle
 '(change-cursor-mode 1)) ; Turn on change for overwrite, read-only, and input mode
(custom-set-faces
 ;; custom-set-faces was added by Custom.
 ;; If you edit it by hand, you could mess it up, so be careful.
 ;; Your init file should contain only one such instance.
 ;; If there is more than one, they won't work right.
 '(region ((t (:background "light gray" :distant-foreground"gtk_selection_fg_color")))))

(defun toggle-cursor-color ()
  (if (equalp "deep pink" (face-background 'cursor))
      (set-cursor-color "Dark Turquoise")
    (set-cursor-color "deep pink")))

(add-hook 'overwrite-mode-hook 'toggle-cursor-color)