pcb design - What should I put on my almost empty PCB layer?

I have a 3"x3" 4-layer PCB where my stack up is:

Signal 1
Ground
5v Power
Signal 2

My Signal 1 layer has a few traces that carry 500 MHz on them, some high resolution ADCs, and microcontroller/usb circuitry. I have SMA connectors that are carrying the 500 MHz on to the board. Currently this will just be "open air" sitting on a test bench, but long term into will end up in a case in which everything will be contained internally.

My Signal 2 layer has almost nothing on it, specifically it has the following:

• MCLR from programmer connector that is 0.1" long


• SPI Data and Clock line that are both about 0.1" long


• Negative voltage (for powering 2 op-amps) trace that is about 2" long

I feel like it is somewhat of a waste to have so much unused PCB. I am considering the following options:

1. Fill the layer with my negative voltage rail


2. Fill the layer with ground


3. Leave the layer empty

Is there any benefit of one of the options over the other? What is usually done in these situations?

Some Additional Details

The system will be pulling a peak of 300 mA off of the 5v rail. While the -5v rail will only have about 2 mA load.

Answer

What is typically done in the industry in these cases, assuming that ground-fill practices as shown in other answers does not provide significant benefit, is something called thieving.

Thieving consists of covering large expanses of unused outer layers with a pattern of shapes, usually diamonds or squares, disconnected from one another. Thse shapes are kept away from other features, such as holes, board edges, or traces. The sole purpose of thieving is to improve manufacturability by ensuring a constant PCB thickness given any particular area on the board, say, half a square inch.

Without thieving, the rollers that are used to laminate the layers together will not exert as much force on the copper-starved areas, which could lead to delamination (looks like light spots inside the board).