is this as simple as metering off a standard 18% gray card every few photos (or say every 30 minutes)? Could this be accomplished in post-photo editing software?

The issue here is white balance, and there are basically two options: you can take steps to make sure that the light is always the same color, or you can adjust the white balance to compensate for the changing color of the light. The first option is what @dpollitt mentioned: provide your own light using strobes so that the light always has the same color. If you provide enough light, you'll completely overpower the ambient light and the subject should have consistent color.

The second option is to compensate for the changes. Set your camera to save your photos in RAW format. This will prevent the camera from interpreting the data and giving you what it thinks the is the correct white balance, and you can then adjust the white balance yourself later. That's where the gray card comes in -- place the card just outside the frame, and every so often either move it into the frame or reframe to include the card and take a photo. Including the gray card every 30 minutes is probably fine in the middle of the day, but in the early morning and late evening the sky changes much more quickly than that, so include the card more often near dawn and dusk.

When you import the photos into whatever photo management program you're using, you can go through them and find all the gray card shots. Every photo manager has an option to adjust color temperature based on a neutral gray tone in the photo, so pick the card. After that, you should be able to apply the same adjustments in bulk to the photos following that one, up to the next gray card shot.