do you stop your garmin during your long run?

Long stops yes...like someone else said...coach told me to run for 1.5 hours, not 1:15 plus breaks.  So if I make a bathroom stop, yeah, I stop the watch.

Short stops?  Nope.  If I'm waiting less than a minute at a stop light or whatever...I just don't worry about that.

From a physiological standpoint, I do not think it matters.  Your overall cumulative training workload is what is important and stopping to go to the bathroom during a training run isn't going to change much come race day.  I try not to stop on my long runs and very rarely do.  For me, it's a mental toughness thing.  I feel like I am training my mind to keep going even when I am very tired or in discomfort.  It would just be too easy to walk sometimes so I fight the urge.

If I have to stop for a light or fill a water bottle I do stop my watch.  I do it so I look faster than I really am in my logs.

x3.  I set my garmin to autopause anytime the pace goes over 13 mm.

It doesn't really matter though.  You improve your run fitness by running, running more, and running at a higher intensity.  If you take a 2-3 minute water break every 2 miles...it just means that you'll probably run a little bit quicker while you're running compared to if you didn't stop at all...or maybe allows you to run a little bit farther before you get tired.  At the end of the day, the training stress you create is likely about the same.

Mine was always on autopause, but when I think about it, I'd should have prolly just let it run. That gives one an greater understanding of "how long" it takes go a certain distance. Nothing "autopauses" during a race. 

I always trained based on mileage not time. 

I stop it too. I want to see what's going on while I'm working out. Making sure that I'm working at an appropriate level for the desired time. Most of the time, the little breaks at a light or intersection mean next to nothing towards training adaptations as they're just getting the training time in. For harder efforts or times when the interruptions would mess with a set or workout, I try to make the route so that there aren't any interruptions in it. Or as few as I can.

If I'm doing speedwork, then I lap everything of consequence (intervals and the rest periods between), so it doesn't matter if I stop for a minute during the warmup or cooldown runs, as the few seconds one way or another don't affect the workout.  For distance, I let it run and look at the overall pace.

To me, at least, I think the overall pace including any stops is a better indicator of what one actually ran.  Again, for me, if I stop for even a few tens of seconds, my HR comes waaaay down and I can pick up the pace considerably.  Those little breaks "count" for me.

I saw this over the last couple months on some long runs where I did 8x9' Z4 intervals with one minute walk breaks between (not even stopping altogether).  I'd never done that kind of workout before (always at least jogged b/w intervals) and was shocked at how much greater the recovery is by walking at half the jog pace than a minute of very light jog. I usually finish that workout with 30-60' of Z2 or Z3, and I notice the difference then, for sure!

So, if I'm getting a recovery in the middle of the run, I count that against my overall time (for instance, during the interval workout above I also look at my overall average pace during each interval - that's a fun mindgame on the last couple!!!).

While I do usualy target running for a set time, I usually pick a course that gets me close to that time and go.  If I take a bit longer overall, like a couple minutes for lights/water bottle refills, it doesn't change the overall time that much.  I guess if I was on a treadmill, or doing VERY short laps where I could just quit at the specified total time, then it would change the workout.  However, since I usually pick a course of appropriate length for the target time, I just run.

And run and run and run...  Which is what helps me more anyway.    That said, Strava tells no lies (unless you're in a paceline with a tailwind on the bike). 

Matt