Before you lay out for a new coil there is one thing worth trying. Remove the coil and make sure that the face of the two supporting pillars is clean and free from corrosion and the same for the area on the coil armature (laminations) that sits on the pillars. then reinstall the coil with the necessary 10-14 thou air gap between it and the flywheel.
Best way to set the air gap is to turn the flywheel so that the magnet is at six o’clock, refit the coil pulled as far from the flywheel as it will go and tighten one retaining screw, leave the other just loose. Rotate the flywheel so that the magnet is under the coil, insert your non magnetic air gap gauge (double thickness of old micro fiche or brown luggage label!) between the coil and flywheel and slacken the screw. The magnet will pull the coil down onto the gauge. Tighten both screws and rotate the flywheel to extract the gauge.
Note that the coil must be installed so that the flywheel magnet rotating in a clockwise direction passes the “lump” of the magnetron module first. Genuine Briggs coils are marked inside or outside (can’t remember which!!)
Then do the spark test again and if no spark feel safe to spend forty quid!