That is an ABSOLUTE possibility. Now that you mention it, the exhaust has a constant "tickticktick" sound right under the shift selector (I am missing some kind of sound dampener I think, because I get a lot of noise from that area). When I turn the car off I get the hot exhaust "ping" sound like little peices of stone are bouncing around in your exhaust, although I doubt that is relevant. I also have no lights on my dash besides the constant 'Bulb out' light and a 'Brake failure' light that is illuminated so much I think someone wired it that way on purpose.

I will try your method (yes, the shaking and kicking) and report back tomorrow. I appreciate all the help.