Would you believe me if I said: "They all do that." Ha!
I would do two things. Take a file to the gap on the spark plug. Both the center electrode - the tip should have square corners, and the side electrode - if there is any rounding, it should be make flat where it faces the center electrode. Most plugs can be faced so they will work as new, especially in the old engines where the mixture is not leaned out by dictate from on high.
Second thing would be to run the thing in the dark to see if you have spark jumping to ground via the secondary wiring. By now, the wires are old enough for a slug of Old Burnside Raw Whiskey, and likely have had some degradation of the insulation and are primed to leak those milliamperes as fast as they can. Be sure also that the ceramic is clean on the outside as any sort of deposit can lead to the spark taking a shortcut. If it has points, use some emery paper folded and trapped using the spring tension to clean off any deposits or oxide. I still have the LAV running on points and I got it used in 1992. Have new points down in the mower parts box. I did clean them once since I got it. Maybe about the time I adjusted the valves when it would not start when warmed up. It seems to start on the first pull if I take off the air filter. New filter media on the way. It does not have a choke I can fiddle with and I do not know how it 'knows' to enrich itself when cold...
tom