Danger2k

2006 RX-8 GT Manual: So 2 months ago, I was going down a very steep hill and since i'm lazy and wanted to go fast, I put the car into neutral. When I got to the bottom of the hill I noticed my CEL was flashing indicating a misfire. So I pulled over, killed the engine, and popped the hood, I started the car back up again, cleared the misfire code, and then shut the hood. When I shut the hood, I noticed a chirping sound. I assumed it would go away, which it did for a month. Then it came back permanently after I installed the K&N Typhoon Air Filter. It only goes away whenever I'm either moving above 1mph in gear, or when the clutch is engaged 2cm or so in. Here's a vid showing the same issue I have:
TL:DR 'Engine misfire in neutral 70mph+, open hood, shut hood, BAM chirping noises'
So, What's wrong guys?