Generally yes — gabapentin and Tylenol (acetaminophen) are not flagged as interacting and are often combined for pain, but stick to dosing limits and check with your pharmacist or doctor.
Neither the NHS gabapentin interactions page nor the MedlinePlus gabapentin page lists acetaminophen (paracetamol/Tylenol) as a medicine to be cautious with. The over-the-counter painkillers that the MedlinePlus gabapentin page flags are NSAIDs like ibuprofen and naproxen — acetaminophen is a different type of painkiller and isn't on that list. Gabapentin's main risk is central-nervous-system effects (drowsiness, dizziness, slowed thinking, loss of coordination), which the NHS ties to strong opioid painkillers such as morphine, not to acetaminophen, which is not sedating. The NHS paracetamol page likewise lists its own interactors (warfarin, flucloxacillin, metoclopramide/domperidone, other paracetamol-containing products) and does not mention gabapentin.
Keep acetaminophen within label limits — for most adults that means not exceeding the maximum daily dose on the package, and crucially not "doubling up" by also taking cold-and-flu or other combination products that already contain acetaminophen (the NHS warns this is the main way people accidentally take too much). Acetaminophen overdose can seriously harm the liver, so be extra careful if you drink alcohol regularly or have liver problems, and ask a clinician first in that case. Watch for excessive drowsiness, dizziness or unsteadiness — but those come from gabapentin itself (especially when starting or increasing the dose, or if you also take opioids, sleep aids or alcohol), not from the acetaminophen. Tell your doctor and pharmacist about all your medicines, including over-the-counter ones and supplements, and check with them before combining if you're pregnant, have kidney or liver disease, or are unsure about dosing.
This is general reference, not medical advice, and not a guarantee of safety. Interactions depend on your doses, health conditions, and other medicines. Always confirm with your pharmacist or doctor before combining products, and follow the dosing on each label.