First is continuity through the points and condensor half going through connection lead and the engine body then the other way through coil to the engine.
FWIW, most any B&S engine built since the mid 50's - 60's uses one of their 4 standard sizes of ignition coils of which all of them have modern solid state equivalents that drop right in eliminating the point and condenser part of the ignition circuit.
To find one used just look for a engine, horizontal and vertical designs still use the same coils, that uses the same base block design/HP rating range and same flywheel size as yours. ~2.5 - 3.5 HP is the small block and flywheel, 4 - 6 HP is the medium small, 7 - 10 HP is the medium large and 11 and up are the large blocks and flywheels.
Also, even if you can't find the same you can usually cheat being they are all the same basic core and coil. The flywheel end radius of the cores are what is different and that can be cheated up or down one size without problems. I've done it to put a coil from a 5 HP on a 3.5 HP a few times. Same with using a old 8 HP on a 12 HP once.
Whenever I am at the scrap yard dropping off a load of metal or whatever I make a point to pull any I can find off junk engines while there just because they are so easy to pull and reuse on other engines I have laying around or to give to others who need one to get an old engine running again.
Looks like the same block as the 3 and 3.5 HP engines I have so more than likely the solid state magneto off junk B&S 3 - 3.5 HP vertical shaft push mower would fit it just fine if you ever go hunting for one.
When testing the coil primary it should look like a ~ 1 - 2 ohm resistance (I think). The secondary HV side should be a several hundred ohms or more and if everything is set right on a good pull you should be able to geta light to moderate ~1/8" - 3/16" spark off the HV lead to the case. Some will do more some won't. Either way if it can fire the plug and it hurts a bit when you touch it, it's good enough.
As for setting the points, full open should be about the thickness of a matchbook cover or just a bit wider.
The primary is the wire going to the points an condensor. Secondary goes to the spark plug.
Just push the spring down with a needle nose pliers.
Odds are everyting is fine and points just got worn or corroded so checking resistances won't tell you anything of value. Magnetos are very simple so if the points are opening correctly either they work or they don't to and if they don't you just put a new one on.
A common fingernail file cleans up points quite well.
I've done that a number of times at antique shows to get guys old engines running on things.
It always bewilders me how many people collect old stuff yet have no clue how to service even the basics of it anymore.
Also if you ever work on something that has a habit of burning or wearing out one point faster than the other it's most often caused by a mismatched condenser.
Every ignition system is a simple LC tank circuit that wants to resonate at a specific frequency so having too much or too little capacitance affects it a lot and causes the points to have to carry more current than they need to every time the circuit fires.