It doesn’t need to assemble a large and complex shader node tree to make a parallax shader in Blender. The simplest parallax effect can be achieved by connecting just 3 nodes.
Add a “Texture Coordinate” node (shift+a – Input – Texture Coordinate) to the shader node tree and connect two outputs of this node: “UV” and “Reflection” with the “MixRGB” node (shift+a – Color – MixRGB). The “MixRGB” node mode should be “Add”.
Link the “MixRGB” node output to the “Vector” input of the texture node that needs to be with a parallax effect.
The parallax strength can be controlled through the “Factor” field of the “MixRBG” node.
These nodes work both in the Cycles render engine and in the EEVEE.

.blend file on Patreon