Apple Pencil (Gen 2) Won't Connect

I bought a refurbished Apple Pencil a month or so ago. I've had a few hiccups since then, but nothing of major concern until today. I went to go use my apple pencil and it wasn't connecting, so I unpaired it from my iPad, expecting it to show up on bluetooth so I could pair it again. Now it won't show up on bluetooth at all. I've left it charging for most of the day and it still won't appear. When I attach it to the side of my iPad it will show the apple pencil icon spinning, but it disappears after about a minute or so. I've restarted the iPad multiple times and done a soft reset, and it still won't show up to pair. I don't think it's the pencil's battery, because I've been using it consistently since I've had it. Anyone have an idea to fix the issue? I don't really want to call Apple Support, but that's what it's looking like as of now.