Timing is also key. If the officer requests for materials, you should be fine to say, go into the glove compartment at that point, as opposed to reaching when it wasn't prompted. Do keep your motions smooth and slow though.
Another thing to suggest is if you're pulled over at nighttime or in low light/dark conditions, turn on the interior lights to the front seats! I've seen officers follow your hands with their flashlights, but with the front cabin fully lit, it does put them at better ease, causing less issues.