Quantifying “how much” I’m going to guess you mean within a session in my response. A full session of only functional training is entirely appropriate. It depends on the client’s goals as to what else should be included, but everyone needs functional work. If there’s no carry over to daily activities, what good is our exercise in improving the quality of life outside the gym?
For many clients, the only time they’ll do functional work is under the guidance of a trainer. These aren’t always the glamorous exercises! They’re the little things that are out of a client’s comfort zone strengthening their weak links that they need, but don’t prefer to do on their own!
However, if you had a senior citizen who needs focus on bone density and strength a dose of traditional exercise done safely on machine weights that allows them to use heavier weights is just as important in their training time.
I’m assuming this “gym client” resides outside of the gym :)…Any training that includes exercises/movement patterns that resemble and strengthen everyday or common demands is more than appropriate; it’s critical!! Our bodies are designed for all sorts of simultaneous movements (planes, joints, muscles); we should work toward keeping that the case for all clients (to whatever degree it is possible and appropriate).
Any training the elicits neuromuscular adaptations is going to be functional. Whether your improving motor patterns, or increasing lean muscle tissue each is going to be functional to the human body. People misinterpret functional training. The movement of the human body is functional and exercise training to help contribute to more efficient movement will result in a functional outcome.