3d printer MOSFET can't use on car bulb, but can use on other load (ie. LED, dc motor, relay)
Do you have a part number for the power switch (which is visibly more than just a MOSFET). It MAY be that it has intelligent protection and that it sees the very low bulb resistance and consequent massive inrush current as a short circuit and "refuses" to turn on. 

The switch is labelled "50 ohms max" -  suggesting that a load at 12V of under 1 Ohm would be tolerated. TRY adding say 1 Ohm in series with the bulb to start with. This increases the load's startup resistance from maybe 0.1 Ohm and may persuade the switch to operate. 

IF this works , see how low a series R it will work with.