Gil 1965 sparkless Valiant

Bozwel said
the condenser has quite a profound effect on the spark. it helps the magnetic field in the coil collapse quicker producing a bigger spark

It actually does more than that. The coil / condenser trade energy "several times" known as "ringing" or tank circuit "flywheel effect."

In the diagram, what is called "coil oscillations" are the trading back and forth between cap and coil. You cannot see this during the spark which is the flat line to the left. If you unhook a plug wire, you can see it clearly