Back when I had a '56 Chevy pickup with a 235 six ,it often refused to fire up sometimes,like it had no spark..
My dad showed me how the distributor cap would build up a black sooty deposit in the coil wire socket--cleaning that crud out with a wire brush usually got it to fire right off again--he said many cars with points did that back in the day..
When I had first got the truck,there was a yellow thing plugged into the coil wire socket,that the coil wire plugged into--it had a label stating it was a "spark intensifier"...
Basically all it was,was an air gap inside the unit,so the spark had to jump across the air gap,and it would also jump across the spark plug gap at the same instant,this would allow even badly gas fouled plugs to fire (like if the engine got flooded by using too much choke)..we took it off thinking it was just a useless thing,but with it installed the engine did start almost every time instantly and ran much peppier.
So,perhaps when you put the spark tester in line with the plug wire,it did much the same thing,seeing the tester is just an air gap--and made the spark jump across the spark plug and fire it off..
I agree it may just need a good de-carboning,it may have sticky valves ,especially if it sits around a lot in between uses..Seafoam or Marvel Mystery oil in the fuel & crankcase and some poured down the intake at fast idle may help a lot...if not,then it may need major repairs..