Synthesis of these sorts of circuits is quite a puzzle, yes.
The general plan of this one is an oscillator, of course, more specifically a multivibrator.
Q1A and Q2A, along with R1, C1 and R2, R8, makes a complementary "differential pair". This is an interesting motif because, though it makes a terrible diff pair (there's a 2*Vbe offset!), the "tail" current -- rather than being sourced from somewhere, then steered between the pair -- is itself what's being sourced. So this can turn on very aggressively, without requiring almost any quiescent current.
You can also think of it as a common emitter amplifier with a fixed offset, which is apparent in this application:
https://www.seventransistorlabs.com/Images/LED_Light2.pngthe top-left NPN could be replaced by a (rather beefy) resistor divider, serving as threshold voltage for its companion. In this case, the resistor divider can be hFE times larger, saving on bias current!
Anyway, Q2A connector drives Q3A base, turning on the main switch. To hold it on, D1, R4 applies positive feedback. (Note another feature of the "complementary diff pair", the bases conduct forward, so C1 gets discharged through D1 and Q3A base.) Q3A remains on (via R1 and R4 into Q1A, Q2A), with base current set by Q1B (a Vbe current limiter -- note that it shunts the capacitor directly, so capacitor discharge current actually flows through Q1B).
Eventually, SH1 voltage rises to a Vbe, turning on Q3B and turning off Q3A. When Q3A collector voltage begins to rise, positive feedback snaps everything off (with a little help from C2) and the circuit resets to its initial timing state (C1 charging through R1).
Note that C1 ends up discharged (down to a few volts) during the on-pulse, which implements holdoff compared to a free-running oscillator like you'd have in a typical peak-current-mode controller like UC3842.
I don't think Q2B is actually doing anything right now, I mean with components and values as shown; but it's supposed to provide another little burst of positive feedback, with D3 increasing the B1 "on" voltage, and C4 triggering Q2B triggering Q3B to turn off Q3A more rapidly.
That's a long story for two halves of a waveform, but so what? I called it a multivibrator, because it is -- there are two important time constants, R1*C1 and T1 and R17 (sort of). This works fundamentally the same as a two-transistor multivibrator, which uses two RC time constants. This kind of flips it, and uses some other fancy blocks (like the complementary "diff" pair, and the peak current mode switch), to use an RC and RL time constant instead. The L of course being necessary for the intended function.
Tim