In order to get the most accurate resting heart rate, should I be at total rest (standing still or sitting) or keep walking during the 2 minutes after my run?
Max
Just stand up still for two minutes to keep the heart rate accurately going down as much as it can without having to cater for extra body motion. The more it comes down from the max HR when you stopped the timer the fitter you are. If you do a warm down during a workout your max heart rate recovery will not be accurate compared to stopping the clock dead on the end of an activity.
I would stop the timer to get the heart rate recovery value then simply add a separate session for a warm down. Some watches do not record RHR. You can see the values after saving a workout on GARMIN on the RUNALYSE platform: www.runalyse.com probably the most comprehensive sport application, takes a while to get used to, but far more data than others.
See your RHR values at the bottom of a full analysis page by clicking on the title of an uploaded workout, you’ll also see your ‘heart rate variability’ broken down if your heart strap supports it. GARMIN ‘running’ & ‘pro’ heart straps do from my experience. Good luck..