Flashlights could be a bunch of portable methods and heuristics that can help on a wide range of problems, not just under one streetlight. Polya's book is an example, as are some of the methods of statistical learning and Feynman's "visualize a hairy green sphere" trick.

The process of coalescing, separating off, or starting new disciplines or (sub-)fields. The necessity and immediacy of this can vary.

Examples:

Vectors/linear algebra/etc.—Necessary because these are minimally and sufficiently complex formalisations/frameworks for intuitive ideas. Immediate because these areas were developed for immediate use on solving linear equations/kinematics/theoretical physics.

Cell biology—Necessary, not particularly immediate: Once the existence of cells was known, it was an obvious next step to analyse them into components, and cells are complicated enough that this necessitates a new sub-field, but the cell model was not a formalisation/framework for an existing intuition; it was an unexpected discovery, and so was of course not pursued to solve a problem at hand (indeed, since it was not known in advance, it was not pursued at all), and possibly (not an expert) did not yield significant use for some time.

Mathematics—Infamous for spawning seemingly-useless-but-decades-later-turn-out-to-be-the-key-to-everything sub-fields. So often not immediate. Necessity is difficult to tell: Addition could plausibly be a necessary concept for sufficiently advanced intelligences, but, say, quaternions are very probably not.

Newtonian mechanics—Possibly necessary, immediate: It's possible that Newtonian mechanics is necessary for most intelligent species on the way to sufficiently advanced physics. Immediate because IIRC Newton's initial speculations were more towards the theoretical/'idle' natural philosophy side, but that they were quickly commissioned by Halley for immediate use.

Freudian psychoanalysis—Unnecessary, immediate: If the LW consensus is correct, then this is both an asspull and useless. It is immediately used to try to treat people.

FAI—Possibly necessary, immediate: For species that are sufficiently 'goal-driven', recursive self-improvement of the species or its constructed successor(s) seems necessary. In the latter case, FAI is intended to solve the problem of solving problems, so is immediate.

~~~~~~~~

Each discipline is a way of lossily zooming in on a particular part of the territory. New disciplines are created by new ways to lossily zoom in. Sometimes discplines split off as similar but still significantly different ways of lossily zooming in. Or if you like, each discipline is a language game that is (hopefully) useful to understand some things; sometimes new language games pop up; sometimes language games spin off others.

Philosophy, being the therapy concerned with the logical clarification of thought, is the incubator for and gives away a disproportionate variety of new fields. Examples: Logic, metamathematics, causality, theoretical physics, biology, chemistry, penology.

I'd think that calculus would be a perfect example. A mathematical analysis technique that's broadly applicable to a wide variety of fields.