From the Stanley IntelliSensor™ Stud Sensor instruction manual.

Calibration:

• Hold the IntelliSensor™ Stud Sensor flat against the surface, making firm contact.
• Locate the activation switch on the right-hand side of the unit – press and hold in. The red LEDs will briefly flash and the green LED “Power” light will go on and remain on. Keep holding the activation switch during all of the following procedures.

Note: While calibrating, the IntelliSensor™ Stud Sensor must not be placed directly over a stud, dense material such as metal, or over a wet or newly painted area, or it will not properly calibrate. Move to a different location and try again

Usage:

• Slide the IntelliSensor™ unit slowly across the surface in a straight line.
  As it moves closer to the stud, red LEDs will go on. When it detects the stud edge, the top LED will go on and an audio tone will sound.

  

• Use the handy pencil hole marker on the IntelliSensor™ unit to mark the stud edge.

• Double check stud location by coming from the opposite direction. Make additional markings. The midpoint of the two marks indicates the stud center.

  

Cautions on Operating:

The proximity of electrical wiring or pipes to the surface of the wall may cause the IntelliSensor™ unit to detect them as studs. You should always use caution when nailing, cutting or drilling in walls, ceilings and floors that may contain these items. Always remember that studs or joists are normally spaced 16 inches or 24 inches apart and are 1-1/2 inches in width. To avoid surprises be aware that anything closer together or of a different width may not be a stud, joist or fire break.

Surface Differences

Wallpaper

There will be no difference in the function of the IntelliSensor™ Stud Sensor on surfaces covered with wallpaper or fabric unless the coverings used contain metallic foil or fibers.

Plaster and Lath

Unless lath and plaster construction is excessively thick, there will be no problem with proper functioning of the IntelliSensor™ unit.

Ceilings

When dealing with a rough surface such as a sprayed ceiling, utilize a piece of cardboard when scanning the surface. Run through the calibration technique described earlier with the piece of cardboard too, to assure best performance of the unit. Also, it is particularly important in this application to remember to keep your free hand away from the unit.

Specifications

Utilizing the procedure of scanning and marking from two sides, the IntelliSensor™ unit will find the stud center within 1/8" accuracy for wood and 1/4" accuracy for metal.

When measuring a wood stud under 3/4" drywall, it is recommended the IntelliSensorTM to be used at 35-55% relative humidity.

I don't know what the right answer is, but I'd probably go with attaching an adhesive screen, using non-shrinking plaster/spackle over that to fill in the area, then trying to tool the surface to vaguely resemble the rest of the design. If you were trying for a museum-quality repair the answer would probably be to actually take a mold of the opposite side and use that to replicate the leaf pattern, but I couldn't advise you on how.

Fixing butchered art is never easy.