Improve Lisp-level documentation of tooltips

* doc/lispref/display.texi (Tooltips): New section.  (Bug#23246)
(Display): Update the chapter menu.
* doc/lispref/text.texi (Special Properties): Make the "tooltip"
index entry more concrete.  Change the cross-reference to point to
"Tooltips" in the ELisp manual.
* doc/lispref/elisp.texi (Top): Update the master menu.
* doc/emacs/frames.texi (Tooltips): Include more customization
variables.  Add a cross-reference to the ELisp manual.

doc/emacs/frames.texi

@@ -1152,11 +1152,11 @@ change the variable @code{x-gtk-file-dialog-help-text} to @code{nil}.
 @section Tooltips
 @cindex tooltips
 
-  @dfn{Tooltips} are small windows that display text information at
+  @dfn{Tooltips} are small special frames that display text
-the current mouse position.  They activate when there is a pause in
+information at the current mouse position.  They activate when there
-mouse movement over some significant piece of text in a window, or the
+is a pause in mouse movement over some significant piece of text in a
-mode line, or some other part of the Emacs frame such as a tool bar
+window, or the mode line, or some other part of the Emacs frame such
-button or menu item.
+as a tool bar button or menu item.
 
 @findex tooltip-mode
   You can toggle the use of tooltips with the command @kbd{M-x
@@ -1164,11 +1164,41 @@ tooltip-mode}.  When Tooltip mode is disabled, the help text is
 displayed in the echo area instead.  To control the use of tooltips at
 startup, customize the variable @code{tooltip-mode}.
 
-@vindex tooltip-delay
+The following variables provide customization options for tooltip
-  The variables @code{tooltip-delay} specifies how long Emacs should
+display:
-wait before displaying a tooltip.  For additional customization
+
-options for displaying tooltips, use @kbd{M-x customize-group
+@vtable @code
-@key{RET} tooltip @key{RET}}.
+@item tooltip-delay
+This variable specifies how long Emacs should wait before displaying
+the first tooltip.  The value is in seconds.
+
+@item tooltip-short-delay
+This variable specifies how long Emacs should wait before displaying
+subsequent tooltips on different items, having already displayed the
+first tooltip.  The value is in seconds.
+
+@item tooltip-hide-delay
+The number of seconds since displaying a tooltip to hide it, if the
+mouse doesn't move.
+
+@item tooltip-x-offset
+@itemx tooltip-y-offset
+The X and Y offsets, in pixels, of the left top corner of the tooltip
+from the mouse pointer position.  Note that these are ignored if
+@code{tooltip-frame-parameters} was customized to include,
+respectively, the @code{left} and @code{top} parameters.  The values
+of the offsets should be chosen so that the tooltip doesn't cover the
+mouse pointer's hot spot, or it might interfere with clicking the
+mouse.
+
+@item tooltip-frame-parameters
+The frame parameters used for displaying tooltips.  @xref{Frame
+Parameters,,, elisp, The Emacs Lisp Reference Manual}, and also
+@ref{Tooltips,,, elisp, The Emacs Lisp Reference Manual}.
+@end vtable
+
+For additional customization options for displaying tooltips, use
+@kbd{M-x customize-group @key{RET} tooltip @key{RET}}.
 
 @vindex x-gtk-use-system-tooltips
   If Emacs is built with GTK+ support, it displays tooltips via GTK+,

doc/lispref/display.texi

@@ -34,6 +34,7 @@ that Emacs presents to the user.
 * Character Display::   How Emacs displays individual characters.
 * Beeping::             Audible signal to the user.
 * Window Systems::      Which window system is being used.
+* Tooltips::            Tooltip display in Emacs.
 * Bidirectional Display:: Display of bidirectional scripts, such as
                              Arabic and Farsi.
 @end menu
@@ -6968,6 +6969,81 @@ indicator of Emacs capabilities on a given display type.  Instead, use
 @code{display-graphic-p} or any of the other @code{display-*-p}
 predicates described in @ref{Display Feature Testing}.
 
+@node Tooltips
+@section Tooltips
+@cindex tooltips
+@dfn{Tooltips} are special frames (@pxref{Frames}) that are used to
+display helpful hints (a.k.a.@: ``tips'') related to the current
+position of the mouse pointer.  Emacs uses tooltips to display help
+strings about active portions of text (@pxref{Special Properties}) and
+about various UI elements, such as menu items (@pxref{Extended Menu
+Items}) and tool-bar buttons (@pxref{Tool Bar}).
+
+@defun tooltip-mode
+Tooltip Mode is a minor mode that enables display of tooltips.
+Turning off this mode causes the tooltips be displayed in the echo
+area.  On text-mode (a.k.a.@: ``TTY'') frames, tooltips are always
+displayed in the echo area.
+@end defun
+
+@vindex x-gtk-use-system-tooltips
+When Emacs is built with GTK+ support, it by default displays tooltips
+using GTK+ functions, and the appearance of the tooltips is then
+controlled by GTK+ settings.  GTK+ tooltips can be disabled by
+changing the value of the variable @code{x-gtk-use-system-tooltips} to
+@code{nil}.  The rest of this subsection describes how to control
+non-GTK+ tooltips, which are presented by Emacs itself.
+
+Since tooltips are special frames, they have their frame parameters
+(@pxref{Frame Parameters}).  Unlike other frames, the frame parameters
+for tooltips are stored in a special variable.
+
+@defvar tooltip-frame-parameters
+This customizable option holds the frame parameters used for
+displaying tooltips.  Any font and color parameters are ignored, and
+the corresponding attributes of the @code{tooltip} face are used
+instead.  If @code{left} or @code{top} parameters are included, they
+are used as absolute frame-relative coordinates where the tooltip
+should be shown.  (Mouse-relative position of the tooltip can be
+customized using the variables described in @ref{Tooltips,,, emacs,
+The GNU Emacs Manual}.)  Note that the @code{left} and @code{top}
+parameters, if present, override the values of mouse-relative offsets.
+@end defvar
+
+@vindex tooltip@r{ face}
+The @code{tooltip} face determines the appearance of text shown in
+tooltips.  It should generally use a variable-pitch font of size that
+is preferably smaller than the default frame font.
+
+@findex tooltip-help-tips
+@defvar tooltip-functions
+This abnormal hook is a list of functions to call when Emacs needs to
+display a tooltip.  Each function is called with a single argument
+@var{event} which is a copy of the last mouse movement event.  If a
+function on this list actually displays the tooltip, it should return
+non-@code{nil}, and then the rest of the functions will not be
+called.  The default value of this variable is a single function
+@code{tooltip-help-tips}.
+@end defvar
+
+If you write your own function to be put on the
+@code{tooltip-functions} list, you may need to know the buffer of the
+mouse event that triggered the tooltip display.  The following
+function provides that information.
+
+@defun tooltip-event-buffer event
+This function returns the buffer over which @var{event} occurred.
+Call it with the argument of the function from
+@code{tooltip-functions} to obtain the buffer whose text triggered the
+tooltip.  Note that the event might occur not over a buffer (e.g.,
+over the tool bar), in which case this function will return
+@code{nil}.
+@end defun
+
+Other aspects of tooltip display are controlled by several
+customizable settings; see @ref{Tooltips,,, emacs, The GNU Emacs
+Manual}.
+
 @node Bidirectional Display
 @section Bidirectional Display
 @cindex bidirectional display

doc/lispref/elisp.texi

@@ -1380,6 +1380,7 @@ Emacs Display
 * Character Display::       How Emacs displays individual characters.
 * Beeping::                 Audible signal to the user.
 * Window Systems::          Which window system is being used.
+* Tooltips::                Tooltip display in Emacs.
 * Bidirectional Display::   Display of bidirectional scripts, such as
                               Arabic and Farsi.
 

doc/lispref/text.texi

@@ -3202,12 +3202,11 @@ or shorter, higher or lower, wider or narrow, or replaced with an image.
 
 @item help-echo
 @kindex help-echo @r{(text property)}
-@cindex tooltip
+@cindex tooltip for help strings
 @anchor{Text help-echo}
 If text has a string as its @code{help-echo} property, then when you
 move the mouse onto that text, Emacs displays that string in the echo
-area, or in the tooltip window (@pxref{Tooltips,,, emacs, The GNU Emacs
+area, or in the tooltip window (@pxref{Tooltips}).
-Manual}).
 
 If the value of the @code{help-echo} property is a function, that
 function is called with three arguments, @var{window}, @var{object} and