mosfet gate different voltages along trace
The connection to the gate is open circuit (bad header, open trace, bad solder joint, something like that) so your multimeter internal resistance is discharging the gate capacitance and switching the MOSFET. 

To prevent this sorta-working situation (among other things) it's good practice to put a high value resistor (such as 100K) between MOSFET gate and source near to the MOSFET. That way it will be reliably off if the connector is unplugged. It won't be a problem with a smallish LED, but if you had a substantial load on the MOSFET in comparison to its ability to dissipate heat, the MOSFET could be damaged by the input floating such that the MOSFET turns partially on. Since an SOT-23 MOSFET can switch amperes, this is not a silly concern. 







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