mouse click on an overlay, using overlay `keymap' property

[Drew Adams]

Could someone please explain what's happening here, and why? How can I get
the overlay's keymap to be in effect over all of the visual (displayed) area
of the overlay?

(setq foo-map (make-sparse-keymap))
(define-key foo-map [mouse-2] 'bar)

(defun foo (beg end)
  (interactive "r")
  (let ((overlay (make-overlay beg end)))
    (overlay-put
     overlay 'display
     (propertize "xxxxxxxxx" 'face 'font-lock-constant-face))
    (overlay-put overlay 'keymap foo-map)))

(defun bar (event) (interactive "e") (message "BAR"))

Here's some text: aaaaaaaaaaaaaaaaaaaaaaa

Select one or more of the a's and do M-x foo, to apply the overlay to just
those a's.

Put point somewhere outside the displayed "xxxxxxxxx" overlay.

Click mouse-2 anywhere on the displayed "xxxxxxxxx". What happens, it seems,
is that, since point is not on the a's that have the overlay, keymap foo-map
doesn't apply. Clicking mouse-2 therefore just calls the default mouse-2
binding, e.g. mouse-yank-at-click. That sets point so that it is at the
beginning of the overlaid text, so that a second mouse-2 click on the
displayed "xxxxxxxxx" does call bar.

If that's what's happening, how can foo be defined so that a first click on
the displayed "xxxxxxxxx" calls bar?

I'm probably not understanding this well - help appreciated. I'm guessing
that the mouse click on the overlay is noted not as being a click on a
buffer position that has the overlay but on a buffer position that is under
the displayed "xxxxxxxxx" but is actually outside the text that has the
overlay.

What I'm looking for is for the click to be perceived by Emacs as happening
on the overlay, and for the overlay's keymap to apply over the full extent
of the overlay, not just at its beginning, causing the overlay's keymap
binding to take effect.

[Note that I'm specifically asking about overlays here, not text properties.
I know how to create clickable text using text properties.]