I intend to apply the attached patch to master.  Its ChangeLog goes
as below.  Comments and suggestions welcome.

Thanks, martin

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Fix some tooltip related problems

Replace 'tooltip' frame parameter with a 'tooltip' member in
the frame structure.  For GTK+ builds use 'tip_last_frame' to
find the frame for which the currently visible tooltip was
made.  For modeline help-echoing have tooltips show applicable
actions only.

* lisp/bindings.el (mode-line-default-help-echo): New function
as default value of homonymous option.
* src/dispextern.h (tip_frame, tip_window): Remove
declarations.
* src/frame.c (make_frame): Initialize new frame structure
member 'tooltip'.
(Fframe_list, other_frames): Rewrite with new macro
FRAME_TOOLTIP_P.
(syms_of_frame): Remove Qtooltip.
* src/frame.h (struct frame): New member 'tooltip'.
(FRAME_TOOLTIP_P): New macro.
* src/gtkutil.c (xg_prepare_tooltip, xg_hide_tooltip): Rewrite
using boolean return values.
* src/nsfns.m (tip_frame): Remove declaration.
* src/w32fns.c (w32_display_monitor_attributes_list)
(w32_display_monitor_attributes_list_fallback): Rewrite with
new macro FRAME_TOOLTIP_P.
(tip_last_string, tip_last_frame, tip_last_parms): New Lisp
scalars replacing Lisp vector last_show_tip_args.
(x_create_tip_frame): Set new frame's 'tooltip' structure
member to true, remove setting of Qtooltip frame parameter.
(x_hide_tip): Additionally test tip_frame for liveness.
(Fx_show_tip): Handle last_show_tip_args to tip_last_frame,
tip_last_string and tip_last_parms conversion.
(syms_of_w32fns): staticpro tip_last_frame, tip_last_string
and tip_last_parms instead of last_show_tip_args.
* src/w32term.c (w32_read_socket, x_new_font): Rewrite with
new macro FRAME_TOOLTIP_P.
* src/w32term.h (tip_window): Add external declaration.
* src/xdisp.c (x_consider_frame_title, prepare_menu_bars)
(should_produce_line_number): Rewrite with new macro
FRAME_TOOLTIP_P.
(note_mode_line_or_margin_highlight): If
`mode-line-default-help-echo' specifies a function, call it to
produce help echo string.
* src/xfns.c (x_make_monitor_attribute_list)
(Fx_display_monitor_attributes_list): Rewrite with
new macro FRAME_TOOLTIP_P.
(tip_last_string, tip_last_frame, tip_last_parms): New Lisp
scalars replacing Lisp vector last_show_tip_args.
(x_create_tip_frame): Set new frame's 'tooltip' structure
member to true, remove setting of Qtooltip frame parameter.
(x_hide_tip): Rewrite with additional tests of frames for
liveness and taking into account that for GTK+ tips the
reference frame is now stored in tip_last_frame instead of
tip_frame.
(Fx_show_tip): Handle last_show_tip_args to tip_last_frame,
tip_last_string and tip_last_parms conversion.  For GTK+ store
FRAME argument in tip_last-frame.
(syms_of_xfns): staticpro tip_last_frame, tip_last_string
and tip_last_parms instead of last_show_tip_args.
* src/xterm.c (x_update_begin, handle_one_xevent, x_new_font)
(x_set_window_size): Rewrite with new macro FRAME_TOOLTIP_P.
* src/xterm.h (tip_window): Add external declaration.