Apple Pencil 2 Connected but Not Working

We have several iPad Pros in the family, so I've had the good fortune of being able to test and rule out some issues here.

The problem is that my daughter's 2nd Gen Apple Pencil will connect to her iPad (or any of the other 11" iPad Pros we have) but it doesn't appear to be sending the proper signal to the iPad that would cause it to work. The iPad is not responding to it in the OS, in Procreate, in Safari... nothing. We have taken the following steps several times:

• Verified the iOS software is up-to-date.
• Visually inspected the pencil for obvious physical damage. There are no cracks or scratches (or even blemishes) on the pencil.
• Removed the tip of the pencil and inspected the nib of the pencil for any obvious physical damage, or dirty/scratched/irregular conductor material. The square conductor on top of the nib appears intact and everything about the gold-colored conductor on this nib appears identical to a working pencil. I gently attempted to clean the nib by blowing on it (thanks Sega Genesis)
• Replaced the tip with a brand new Apple Pencil tip. Verified that the new tip is not an issue, by trying it on a working Apple Pencil. It has no problems. Trying another new tip on the problem pencil also doesn't work.
• Verified it's an issue with the pencil and not the iPad by:
  • Trying other 2nd gen Apple Pencils on my daughter's iPad. They connect and the iPad responds normally to them.
  • Connecting other 11" iPad pros to the problem pencil. None of the iPads respond to it when using it. When we connect another Apple pencil, they work fine.
• Checked to see if the iPads can detect the charge status in different states. The have seemingly accurately detected the pencil in 30-something percent, 90-something percent, and 100 percent charge.
• Went to settings and elected to "Forget this Device" in the Bluetooth menu (making sure it's the problem pencil we're forgetting)
• Reconnected with no luck
• Forgot the device and turned off Bluetooth. Rebooted the iPad. With the Bluetooth off, connected the problem pencil. Got the "Tap to Connect" window, and successfully connected, turning Bluetooth back on. Still no luck. Re-verified that the iPad does work with other pencils.

I'm having a hard time giving up on this pencil because the iPads connect to it. Any suggestions??