>         (defvar teest
>           (let ((map (make-sparse-keymap)))
>             (define-key map "n" #'next-line)
>             (define-key map "p" #'previous-line)
>             map))
>
>         (put 'next-line 'repeat-map 'teest)
>         (put 'previous-line 'repeat-map 'teest)
>...
> 4. Type C-n.  Notice that it does not trigger the repeat map.

I tried to implement what you asked to do, but got horrible results
caused too much damage.  Here is the lossage explaining the problem:

 C-<tab>           ;; tab-next
 o                 ;; tab-next
 n                 ;; gnus-group-next-unread-group

i.e. I typed C-<tab> to switch to the next tab with the text buffer
where I started to type text that begins with the letters "on..."

But instead of inserting letters to the buffer, the letter "o"
switched to the second next tab.  This tab contained the Gnus buffer
where typing the second letter "n" called the bound command
gnus-group-next-unread-group, and I lost all unread messages.

But I never had such a problem when the repeating sequence was
activated only by 'C-x t o ... o o ...' instead of 'C-<tab> o o o ...'
because 'C-<tab>' is a single key, there is no need to activate
other keys doing the same.

This means that by default this behavior should be disabled.
But maybe a new variable should allow to skip this check: