Only way to support a tail like that is having something holding the top part up, like pinning it to your back or using clear string to attach it to your back/necklace/heavily-pinned wig.
What I would do is have a clear string sewn through the back of my bra/harness and shirt (so then the back of my shirt wouldn't pop out much), and have another clip well-sewn directly to the tail, or just something for the clip to clip onto. Then I could remove the tail without removing the costume. There would need to be a large snap or clip at the base of the tail, too.
here's a picture that might make it easier to understand? The second one just shows how you could spread out more strings to make it more stable. Shorter strings would mean it would bounce around a lot less, but it all depends on what look you're going for. This would be easier to fasten than a snap if the tail is really thick.
And a way you could make the tail weigh less if probably making it out of light styrofoam or a chickenwire base, both of which might be hard to cover depending on the fabric you're using. Buuut I'm assuming from your post that you've already made the tail, so oh well.
