I am looking to make an improvement on a product already in place. Is it crucial to build a mock up of what I am proposing? How specific do I need to be with my improvement idea? Do I need to include the exact placement of certain parts or simply propose the idea?
Patents are state-granted monopolies for a limited time in exchange for providing the community (public domain) all elements allowing it to reproduce the invention (especially after the monopoly lapses).
This principle has three consequences that makes building at least a prototype desirable before filing a formal patent:
in most international patent laws, patents must satistify the industrial applicability requirement. If something is wrong in your description and just wouldn't work, the patent could be denied. In US patent law, there is the more or less equivalent principle of utility.
the description must be concrete and detailed enough to allow skilled in the art to reproduce the invention. This is the sufficiency of disclosure principle.
part of the game of patents is to obtain a monopoly as large as possible with broad claims. Building your prototype will help you realize the exact perimeter of the difficulties (the technical problem your invention solves) as well as possible other ways to solve them. It is important to cover those as well.
Timing might drive you to skip the actual implementation of the invention. Yet several mechanisms exist to handle this including provisional applications in the US. Also, typically, since an invention can be improved while being patented (as the inventor is exploiting a working implementation), mechanisms exist to cover these improvements (divisional applications). The golden rule of timing is to not publically disclose how the invention works before filing (there are national variants here including in the US). Yet if a demo reveals too much, it might means the invention lacks an inventive step.
Patent agents and attorneys are specialized in finding the proper minimal disclosure and the proper balance between vague conceptualization and implementation. Cf George White's warning about "proposing an idea" in his reply.
Having a working model is not required. But you do need to explain how to make and use your invention. There may be more than one exact structure that will work but you need to explain at least one way in enough detail that it is clear what you are describing and that it probably works. Do you need to make a working model to convince yourself it will work? Definitely do not say you are "proposing an idea" in a patent application.