Glad you're getting it going. I'm assuming the coil has a spark plug wire attached to it, probably behind that air duct where I couldn't see it.
The PAIR system serves no purpose, other than to satisfy the EPA, and can cause some running and starting issues. It is called the Pulsed Air Injection System, and injects air from the intake system into the exhaust, leaning out the mixture in the exhaust causing it to run hot, and usually backfiring. It is controlled by engine vacuum, and there are several places where a vacuum leak can occur. I have always removed them and plugged everything on every bike I ever had that had one, and they always ran better.
2002 Vulcan 750, 2001 XT225
2008 Vino 125, 2009 Genuine Stella
2012 Zuma 125, 1980 Puch Newport moped