Quantification, control and understanding.
If you don't understand something, it's out of control.
If you can't quantify the causal relationships, you don't understand it.
My (MJMcC) contribution is to develop the quantified models that give you the understanding that you want.

The result may be a simulation you can experiment with, a design calculation method you can use or simply guidance as to practical alternative actions.
Notice the emphasis on 'practical'. Despite the (apparent) devotion to applied mathematics, I'm a "hands on" engineer, through and through. Trained the old-fashioned way as an apprentice, the guiding theme was "if you can't do it yourself, then you've no right to ask anyone else to do it".

Why Models?
    Business interactions in markets and in economics, engineering designs, control systems and manufacturing and supply systems can become complex. If they get so complex that a manager or designer can't estimate the consequences of an action or change in a direct, straight forward, one step at a time manner, due to effects of feedback or closed loop or recycle paths, then some organised quantified approach is needed to elucidate the real underlying causality.
The problem of assessment of effects is made much more difficult if the feedback paths take time to respond; the dynamics of the system have to be accounted for as well. That's my area of expertise. When such a system has been described in quantitative terms you have a model. Then you can understand and assess numerically the effects of changes (the "what ifs") and options. You have quantified the causal relationships.

The consultant as teacher.
It seems to me (MJMcC) that the role of consultant is also that of teacher. It is appropriate that those with experience and knowledge to hand on should try to pass it on to the people with whom they work. In the process the teacher learns even more so there's no loss to anyone. I've been and still am a teacher at undergraduate and graduate level both in the UK and the USA. I enjoy teaching and take care to explain whatever I do to my clients. Ultimately, they have to make choices for themselves; the consultant can really only advise. Since it is essential that clients understand the work done for them and assess it for themselves, the consultant must be a teacher.

Dealing with Complexity: Keep it simple.
All mathematical modelling is based on an argument by analogy. The mathematical model is not the same thing as the part of the real world it represents. No one can prove its equivalence. The validity of any quantitative analysis depends on how closely the numerical (mathematical) model and the reality match. I adopt the principle of parsimony, Occam's razor, and start with the simplest model that has a good chance of being effective enough.
The skill comes in being able to make good estimates (guesses?) early in the modelling work as to how much detail will be needed to get the quality of the match sufficient for the decisions which have to be taken. That's where the experience counts. I've been doing it successfully for more than 40 years.
But, a simulation or mathematical model can become so complex that the mind boggles! The people using it can no longer follow or quite explain how it behaves the way it does. It may be a size issue, but is more likely to be due to strong non-linear cross coupling between components. Once the model has hit the "boggle limit" pushing on with additional complexity, which the intended users, the client and even the model makers, can't assimilate isn't likely to be much help.

Industrial Folklore and the Compelling Force of Reality.
In any established industrial environment, where manufacturing processes have been developed and improved over the years by trial and error, there appear beliefs, "industrial folklore", about how things work, about how processes must be run to make good product. From one shift to another, the supervisors change settings; engineers debate about the importance of controlling particular variables; the customers say the product has changed but everyone says we still make it exactly the same way!

Sometimes the debate about it becomes so heated that it obstructs rational thought. If this is the case, then the circulating industrial folklore, with its inconsistencies needs to be rationalised. My experience has been that as we develop a working, internally consistent mathematical (necessarily quantified) model or simulation and share it with people, the wilder ideas in the folklore somehow disappear and a shared view, soundly based on the real underlying physics or economics (the compelling force of reality) becomes a basis for guided improvement.

Ethics of Consulting
There are ethical issues in consulting. Generally the consultant has some knowledge that will be useful and therefore valuable to the client.
The consultant must not take advantage of special knowledge to the disadvantage of anyone.
The consultant must not take on work which presents a conflict of interest.
The consultant must not take on work which he is not competant to undertake.
The consultant must not pretend that more work is needed than is necessary.
The consultant must not offer any advice that is not in the best interests of the client, even if that is not advantageous to himself.
The consultant must treat all work done for a client as confidential unless express consent to expose it has been given. That's why you don't find a list of clients on this website .. if you want a reference from some other client I'll be able to provide it, with their consent, of course.

I subscribe to the codes of ethics of the professional engineering institutions of which I am a member, the IEEE (USA, Institute of Electrical and Electronic Engineers, Life Member) and the IET (UK, Institution of Engineering and Technology, Fellow).
These codes of ethics cover proper professional behaviour, not only of consultants, but really of any engineer, employee or self employed. In my view they should apply to anyone who has some expertise or knowledge with which he or she could take advantage of those with whom they deal.
That includes horse traders, stock traders and their ilk. Maybe I'd have to make an exception for poker players; they should know what is going on.