Your first generation iPad Pro only supports the first generation Apple Pencil. This Pencil has the removable cap (with a metal band) that exposes the Pencil's Lightning connector used for both pairing and charging.
Here is a link to Apple's definitive compatibility list for iPad and Apple Pencil:
Apple Pencil compatibility - Apple Support
The iPad User Guide includes information about pairing and charging the Pencil with its host iPad:
Pair and charge Apple Pencil (1st generation) with iPad - Apple Support
As described, assuming that the Pencil's battery was healthy, the Apple Pencil should have successfully paired with the iPad when connected. Once paired, inconsistent drawing will either be due to a problem with the Pencil itself, or its interaction with the iPad screen.
Ensure that the user-replaceable Pencil tip is snugly screwed into the body of the Apple Pencil; when fitted correctly you should see a tiny gap, of about the thickness of a sheet of paper, between the tip and pencil body. If slightly loosened, or overtightened, the Pencil may not work properly, if at all.
Be aware that if your iPad screen has ever been replaced by anyone other than Apple, the screen will not be properly calibrated; this situation is known to cause issues with the Pencil. Also, if the Pencil has been dropped onto its tip, or if the tip has been subjected to unnecessary force, the transducer element that its located beneath the replaceable plastic tip may have been damaged; a damaged Pencil cannot be repaired - only replaced.
If your Pencil has been set-aside for an extended period, unused and uncharged, the Pencil battery may have been damaged through deep discharge. In common with all Li-ion batteries, they must always have some level of 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. Do not 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.
Genius Bar Reservation and Apple Support Options - Apple
Gentle warming of the Pencil (such as placing on a hot water radiator), prior to attempting charging of the Pencil, can sometimes resurrect a dead Pencil battery.
