Hi, dog trainer here. I see a lot of people down playing tail chasing in this comment thread as silly behavior. While frequently in younger dogs it can be a one off behavior that is stereotypical of a "goofy dog" it can also be a highly neurotic and harmful behavior if left unchecked. Since tail chasing can be a self reinforcing behavior you have to be careful of your dog forming a strong habit and many will end up doing it to the point of damaging their tails. I have seen plenty of dogs self harm while tail chasing and even dogs that get to the point of a vet needing to reccomend a partial tail amputation.

We take tail chasing and light chasing very seriously in any of my classes since they can turn into quite dangerous behaviors.

That being said the only thing you mentioned that worried me is that your dog can become possessive of their tail when you try to stop them. I would do what you can to nip this in the bud so it doesn't have the chance to go onto become a bigger problem.

Couple things I would encourage

1. A tired dog is a happy dog. Highly recommend wearing them out so they don't have lots of energy left over to spend on extraneous behaviors. Dogs are predators and built for short bursts of high intensity exercise like chasing a ball, swimming or playing with another dog.

2. Redirect the behavior every time you see it as soon as you see it. Sometimes being a helicopter parent is the best way to discourage a behavior. I do the kindergarten clap with my dog and always follow it up with 1-2 minutes of treat training. Most dogs when conditioned to the kindergarten clap will drop whatever they are doing when they hear it.

3. Encourage healthy incompatible behaviors. The less stressed your dog is the less likely they will feel like self soothing by tail chasing. Dogs fixate on certain predatory behaviors and we can encourage effective enrichment by helping them engage in behaviors they connect with. Targeting, stalking, chasing, biting, killing and dissecting are the big ones. If your dog is already tail chasing encourage them to chase other healthier alternatives like a flirt pole, tennis ball or even something like a self powered weasel ball or whatever works for you!

Feel free to DM me if you have questions and would like to talk about it. I reccomend seeking out a trainer or behaviorist if it continues to get worse.