If I understand your question correctly, you’re asking how I go about applying the mental models, and whether it happens instantaneously or takes concerted effort and time.

The answer would be “both” or “it depends”. Sometimes the model to use is obvious and jumps right out at me, and the application could be either instantaneous or take effortful time and action. For example, if I am starting a business that has a probability of success or failure, I might instantly recognize that I have a survivability problem on my hands: the business has to stay operational to continue to have a chance to really take off. Thus I might instantly recognize and apply the model of robustness. But then I might ask myself how to go about achieving that. There, I would apply a commonly used model — inversion — and ask myself, instead, what could I do to ensure that the business would fail? Generating those ideas of activities and choices to avoid would take some time.

Likewise, if I want to know how opening this business might compare to other options, I might apply the model of expected value (essentially basic probability). Knowing to use that model is nearly instantaneous, but applying it and calculating the EVs takes time and effort.

In the example above, inversion and expected value are part of a “frequent” or “standard” list of models that I apply to many situations as lenses of analysis. You can generate and implement such a list yourself: it’s basically a way of looking at reality from many different angles. And the more angles you build into your analysis, the more insight you’ll tend to gain when evaluating important decisions.

But sometimes I run into a problem that I haven’t encountered before. There, I might start playing around with different models to see if doing so gives me a foothold. For example, I might analogize and ask, “what if this thing were a rock and were exposed to incredible pressure over a geologic period of time? How might it change?” Or: “What might happen if I were able to evolve this (idea, system, etc.) over many generations by deselecting unfit parts of it over several generations?” (Essentially applying the model of Darwinian evolution.) Such applications can take hours or could happen in several sessions over days, weeks, months, or even years.

In the last example, it can be helpful to collect, list, and organize the key mental models from as many disciplines as possible, and either run down the list and apply each one to gain insight; pick one at random to apply; or just go with your gut if one feels right to apply. Inspiration and play can and do inform the process!

As a final example, I might have domain-specific models and routines that I apply. If I’m evaluating an appellate law case, I might use the models of timeliness, preservation, waiver, and a series of models specific to prospective-clients (conflict of interest, ability to pay, use of past attorneys, personality) to evaluate whether the case is one I can take and one that I should take. Then, if the client wants a contingency fee agreement, I would apply the model of expected value and then a series of domain-specific models to evaluate probability of success and the probable amount of my fee at the end of the day. Knowing the models to apply and how to apply them is a matter of expertise, which we develop through a combination of study, experience, past failures, and systematic efforts and modifications to improve performance in the future. Some models apply often, some rarely; and sometimes even the same model can either be applied almost instantly or else require a slow, methodical, and laborious process — a process that itself might require the application of other “sub-models”.

I hope my answer has gone in the direction that you intended, and that it is somewhat helpful to you.