Time-resolved fluorescence imaging techniques, like confocal fluorescence lifetime imaging microscopy, are powerful photonic instrumentation tools of modern science with diverse applications, including: biology, medicine, and chemistry. However, complexities of the systems, both at specimen and device levels, cause difficulties in quantifying soft biomarkers. To address the problems, we first aim to understand and model the underlying photophysics of fluorescence decay curves. For this purpose, we provide a set of mathematical functions, called "life models", fittable with the real temporal recordings of histogram of photon counts. For each model, an equivalent electrical circuit, called a "life circuit", is derived for explaining the whole process. In confocal endomicroscopy, the components of excitation laser, specimen, and fluorescence-emission signal as the histogram of photon counts are modelled by a power source, network of resistor-inductor-capacitor circuitry, and multimetre, respectively. We then design a novel pixel-level temporal classification algorithm, called a "fit-flexible approach", where qualities of "intensity", "fall-time", and "life profile" are identified for each point. A model selection mechanism is used at each pixel to flexibly choose the best representative life model based on a proposed Misfit-percent metric. A two-dimensional arrangement of the quantified information detects some kind of structural information. This approach showed a potential of separating microbeads from lung tissue, distinguishing the tri-sensing from conventional methods. We alleviated by 7% the error of the Misfit-percent for recovering the histograms on real samples than the best state-of-the-art competitor. Codes are available online.