You are a steely-eyed rocket man, audioguru. I mentioned the one about the collector resistor, but missed that wretched mess with the MOSFET and blatant lack of a supply for the 555 circuit.
In addition to the floating source (or incorrectly connected drain and missing supply voltage) AND the dismal 20ma of on-state current it could conduct with Vgs = 5V, it will still never work because it's an N-channel device trying to work as a source-follower off a very inadequate voltage. You either need to get a different N-channel mosfet and connect it from ground up, or use a P-channel mosfet there and pull its gate low.