This is something I go through several times a night. Sometimes it is easy, sometimes not so easy.

So this is just a fun exercise to see at what point can you identify this target and make a determination to shoot or no shoot?

No shot safely taken.

Me neither, took to long to tell for sure.

I felt pretty sure it was a canid after I could see it walking and was certain it was, and likely a coyote when I saw it react to the lip squeak, but by that time, it would not stop moving and I could not get a shot even if I would have been confident.

Definitely hard to tell initially. Same problem with hogs and cows long distance...

As soon as it started to move I could tell and definitely after the lip squeek.
Like you, some times its hard to tell when they're standing still with thermal but I've paid a lot of attention to what deer and coyotes do.

These are fun games to play for sure. Initially couldn't tell between deer/coyote due to it being by itself, I am sure if there were deer and coyote you would have been able to tell, but a pack of yotes and a herd of doe wouldn't have helped much if they were all standing still.

Once it started moving it was pretty easy to see it was a dog, but as mentioned, no way to get a good shot as it never stopped and then went into the brush.

Standing animals can be tough, but you get a quick read on them based on their Movement, speed, and travel tendencies. I can pretty reliably pick out hogs from cows from a long way away just based on movement. Coyotes and fawns or line deer can be tough esp in thicker grass where you might not see anything but body and head. Usually behavior is the telling sign here, and how they move. Coyotes trot and deer walk or leap for the most part.

I try not to say "never" but I have rarely seen a coyote bolt unless shot at, they typically trot away whereas a deer may walk away but you will hear then snorting and blowing and it's easy to see, if the run away they will almost always bound out of the area quickly only to be seen trotting later at more distance. Difference between prey animal and predator.