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1) I would recommend to de-install the dimmer switch and re-wire using a standard Single Pole Single Throw ON/OFF switch for the address sign.
2) You mention that the GFCI receptacle is controlled by a dimmer switch, therefore I assume that the dimmer switch is wired upstream of the GFCI receptacle. It is not recommended to wire a dimmer switch in your type of application. Dimmer switches control and vary the voltage levels and are only meant to be used to control a permanent light fixture and never a receptacle of any type or in any location.
In fact, it is a violation of the National Electrical Code to control any type of receptacle via a dimmer switch.
A switched receptacle can only be controlled by a standard Single Pole, or 3-way or 4-way wall (ON/OFF) switch and never a dimmer type of switch. Reason being, if a receptacle is controlled by a dimmer switch and you plug in any non-lighting load, you will destroy the plugged-in load in the receptacle due to the possibility of the varying voltage level originating from a dimmer switch.
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