The 'p' lead is the small kill wire. Its end needs to be well clear of the engine (ground) for testing and the insulation needs to be in good condition. This wire is grounded to 'kill' the engine.
A thin card (business card is another common suggestion for setting up the air gap between the coil frame and the flywheel magnet. Basically it needs to be as close as is sensibly possible to the flywheel without touching.
You're right, the coil doesn't look flash but that's not really an indicatior. It would definitely be worth making sure the earth of the coil to the engine and the wiring terminal under the bolt head is sound. A rub with sandpaper in the usual fashion
