Repeated password entry despite it being visible?

If the signup for a new user account dialog includes an input field to set a custom password which has an option (eye icon) to uncover its current textual contents, should there also be an input field to repeat the password once more which ensures that the user does not mistype it (which uncovering it also does)?

If either a visible password or a repeated password suffices, should the eye icon toggle the repeat password input field?

(This question assumes, of course, that asking the user to repeat their password upon signup is a good UX pattern in the first place. I do not have the possibility to implement a passwordless signup due to organizational restrictions, by the way.)