Bearing in mind that the means of illuminating the neutral light is a switched earth, how can a loose connection turn it on?
I would suspect that the most liklely cause is a fault on the neutral switch, try unplugging the connector & see if the problem persists.
If it does, then you would appear to have a short to earth between the switch & the clocks - look at the connector blocks for corrosion etc & any damage / chafing of the loom.
Andy
