The classic format of the Briggs "Code" (date of production and production plant number) has 8 digits, but I do not assert that it always did. The first 6 digits are the year, month and day of manufacture. At one time Briggs said that these were followed by two digits giving the shift number and plant number, but this does not seem to have applied for very long. Most engines had a zero as the second-last number, but Briggs plant numbers soon exceeded 9 and two digits were required for the plant number. It seems your engine was made in Plant 3, which is the Rolla, Missouri plant. Like most of the old Briggs plants it seems to be closed now - it's closure was announced in 2007.
With regard to the engine stopping device, there were two generations of those plug-top shorting levers. The first ones, used on WW2 lightweight generators, were made from spring steel: you sprung them onto the plug top, and then released them when the engine was stopped. The problem with that design was it did not keep the engine from restarting if it were rotated accidentally. The second generation of the levers was pivoted at the cylinder head end, and used a piece of the cowling as a spring so the shorting lever would either click into the run position - not touching the spark plug - or into the stop position - held against the spark plug by spring pressure. It's been a while since I had one and I don't recall the detail clearly, so my starting point would be to make it look like rolla 16V's one.
Your engine is only 6 cubic inches displacement (100 cc), side valve, with a compression ratio of 6:1 and a maximum speed of 3,600 rpm. Advertised power for the 60102 was 2 h.p. It seems for yours (61202) it was 2.25 hp. That is quite sufficient for a small (14") reel mower, which has very much higher cutting efficiency than a rotary mower. The 17" version used an 8 cubic inch Briggs engine advertised at 3 h.p.
