Hi, if the miss fire is fixed, both may be related, with your rich condition but is usually unlikely. If no check engine light on now, simply just drive it out. If lamp pops up again, then check air filter, all lines before the throttle body to the air filter. If okay, you should look at the MAF sensor, or mass air flow sensor , as a possible problem to your concern. With no starting, or driving concerns, will be unlikely a fuel injector leaking, or excessive fuel pressure.
If no lamp on now, simply drive, and fixing the miss fire likely fixed the p0172. If lamp comes on again let me know. a miss fire can cause a rich condition, and a lean condition. the p0172 may be caused by unburned fuel being monitered by the o2 sensor.
Thanks! By the way, head is the correct term, wire should connect directly to the head, then to a coil pack.