I can't believe how long this went round and round in circles. If joining the brown and blue wires turns the unit on, the blue is not a neutral, it's the switched line as per Moley above (although, as it is inside equipment where BS7671 does not apply, I wouldn't expect it to be sleeved brown).
I don't think it has been said explicity but it looks like the OP is replacing a non-illuminated switch (for which the line and switched line are present at the connector on the PCB) with an illuminated one (which also needs a neutral that is not present). To power the neon, as per Telectrix, a neutral needs to be got (perhaps from the terminals of the IEC inlet, where they project through the PCB).
The equipment is being modified and its safety approvals rendered void, therefore the modifier takes on significant responsibility for safety and compliance. Whatever happens, it must be made practically safe, and an internet forum cannot possibly convey all the details required to guarantee that. I would respectfully suggest that doing modifications to mains-powered equipment by guesswork and experiment, without first being acquainted with the circuit and parts one is attempting to wire up, is not a good idea.