These support pages may be helpful with pairing and use of the Pencil with your iPad:
Connect Apple Pencil with your iPad - Apple Support
Charge your Apple Pencil and check the battery - Apple Support
If you continue to experience difficulties, here is one of the better troubleshooting guides:
https://appletoolbox.com/apple-pencil-not-working-heres-our-troubleshooting-guide/
As described, your Apple Pencil is exhibiting symptoms of a failing/failed battery - that will not reliably accept or hold any charge.
The tiny internal Li-ion battery is susceptible to permanent/irreversible damage through being left discharged for long periods. Even some “new” pencils can exhibit signs of failure out-of-the-box if they are “old stock”. It is essential that if you have an Apple Pencil that you charge it regularly - whether used or not - so as to protect the battery from deep-discharge. Never allow a pencil to remain in low-charge state for any period of time - as the internal battery will fail, rendering the Pencil useless. Setting aside an unused Pencil, for extended periods, is a recipe for premature death of the Pencil battery.
If the Pencil Battery has failed, the only remedy is to replace the Pencil. If the battery has failed and your pencil is within its one-year warranty, you should look to having it replaced by your retailer or at an Apple Store.
You would be best advised to visit the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) - where the technicians will be able to test and assess your iPad and Pencil. If a fault is identified, you’ll be in the best possible place to explore your available options:
Genius Bar Reservation and Apple Support Options - Apple
