Neural Mechanisms of Accumulation and Triggering
There is a model of neural mechanisms of accumulation and triggering in the domain of perceptual choice called the leaky competing accumulator (Usher and McClelland, 2001) model. It uses decision units that fire when sufficient evidence has accumulated. Ratcliff and McKoon (2008) pointed out that LCA associated with their Diffusion model accurately modeled the neural firing rates observed in monkeys before a decision was made (see section 10 of the article, a monkey moving his eyes to a target that competed with a non-target stimulus).

The processes described in LCA are also found in different theoretical account of decision making. You may find some models in this wikipedia page summarizing the decision field theory of Busemeyer &amp; Townsend (1993).

Your question mentioned a longer time scale than the one addressed by the above references. I don't know a model of accumulation/decisions that span over hours/days/years. For example, the one here, despite its promising title ('From perception to action: an economic model of brain processes'), is not interested in the temporal aspect of the decision (i.e. accumulation phase).