Custom Tabline next/prev

init.el

(defun custom-tab-line-switch-to-next-tab (&optional mouse-event)
  "Switch to the next tab - cycle back to the start at the end.
Its effect is the same as using the `next-buffer' command
(\\[next-buffer]). with the exception it will not open a non-visible buffer"
  (interactive (list last-nonmenu-event))
  (let ((window (and (listp mouse-event) (posn-window (event-start mouse-event)))))
    (with-selected-window (or window (selected-window))
      (let* ((tabs (funcall tab-line-tabs-function))
	     (tab-buffers (mapcar (lambda (tab) (if (bufferp tab) tab (cdr (assq 'buffer tab)))) tabs))
	     (num-tabs (length tab-buffers))
	     (tab-position (cl-position (current-buffer) tab-buffers))
	     (next-tab-position (mod (1+ tab-position) num-tabs))
	     ;; find the buffer
             (buffer (nth next-tab-position tab-buffers)))

        (when (bufferp buffer)
	  (if (eq next-tab-position 0)
	      (progn
		(set-window-buffer window buffer)
		(set-window-next-buffers window (delq buffer tab-buffers)))
	    (switch-to-next-buffer window))
	  )))))

(defun custom-tab-line-switch-to-prev-tab (&optional mouse-event)
  "Switch to the prev tab - cycle to the end whe moving past the start
Its effect is the same as using the `prev-buffer' command
(\\[prev-buffer]). with the exception it will not open a non-visible buffer"
  (interactive (list last-nonmenu-event))
  (let ((window (and (listp mouse-event) (posn-window (event-start mouse-event)))))
    (with-selected-window (or window (selected-window))
      (let* ((tabs (funcall tab-line-tabs-function))
	     (tab-buffers (mapcar (lambda (tab) (if (bufferp tab) tab (cdr (assq 'buffer tab)))) tabs))
	     (num-tabs (length tab-buffers))
	     (tab-position (cl-position (current-buffer) tab-buffers))
	     (next-tab-position (mod (1- tab-position) num-tabs))
	     ;; find the buffer
             (buffer (nth next-tab-position tab-buffers)))

        (when (bufferp buffer)
	  (if (eq tab-position 0)
	      (progn
		(set-window-buffer window buffer)
		(set-window-next-buffers window nil)
		;; when clearing the next buffers
		;; emacs reuses them as prev buffers
		;; but in same order
		;; undo the reversal
		(set-window-prev-buffers window (reverse (window-prev-buffers window))))
	    (switch-to-prev-buffer window)) )))))


;; bind the above to keys
(global-set-key (kbd "C-<prior>") #'custom-tab-line-switch-to-prev-tab) ; page up key
(global-set-key (kbd "C-<next>") #'custom-tab-line-switch-to-next-tab) ; page down key

;; rebind tab-line scrolling
(global-set-key [tab-line S-mouse-4]    #'custom-tab-line-switch-to-prev-tab)
(global-set-key [tab-line S-mouse-5]    #'custom-tab-line-switch-to-next-tab)
(global-set-key [tab-line S-wheel-up]   #'custom-tab-line-switch-to-prev-tab)
(global-set-key [tab-line S-wheel-down] #'custom-tab-line-switch-to-next-tab)