My eTrex 30 does not have the pause feature or the auto-pause feature, and it does show GPS drift, but the apparent moving speed when stopped is very low and it is correctly interpreted by Strava as a stop. I have it set to one point per 2 seconds, which results in 0.1-0.3 mph drift.
You should see more drift if your device is connected to a power meter. By default, Edge 500/800 is in a "smart recording mode", meaning that you have longer intervals between points if you're stopped. When you connect to a power meter, it starts recording one point per second.