When you hear tapping in your walls at night it could be a result of mice or rats or even just loose pipes in the wall could be contracting and expanding or even the HVAC system could be making the tapping sounds.
In some cases the tapping in your walls at night could be a termite infestation or problems with the home's foundation.
Rodents such as mice and rats in the walls are common causes of the tapping sounds in your walls at night as their movements and their scratching inside the walls can create the tapping or even rustling sounds within your walls.
Termites can also create tapping sounds or clicking sounds as they tunnel through the wood.
Even other animals could make tapping sounds or other sounds in the walls at night such as birds, bats and squirrels when they find their way into walls and cause the noise.
If it's loose pipes they can expand and contract in the walls with temperature changes, especially if some hot water is running and can cause the pipes to rub against framing or supports in the wall and create tapping noises.
Even water hammer which occurs when water flow is stopped suddenly can cause pipes to vibrate and make banging sounds.
And also ductwork such as with your furnace or central ac system can lead to tapping and clicking sounds which can come through the ceiling or walls or floors depending on where your ductwork runs through.
In some cases the tapping sounds can also indicate that your homes foundation is settling, although it's also often accompanied by other signs of structural issues including drywall cracking or plaster cracking and falling.