How and why does this oscillator work?

Question

I am a beginner hobbyist, trying to understand a circuit from an old Radio Shack electronic snap kits game (the game variant I have is "electronics 303", and the circuit is project #202 : Oscillator 0.5 - 30Hz, in case you ever owned a copy).

When I build the circuit, the LED does indeed blink once every 2 seconds or so for a certain potentiometer setting. However, I can't see any oscillation when I try to simulate it: I used ngspice, my own simulator, as well as the variant from this website. To be fair, I don't know all the simulator parameters for the transistors and LED involved, so I used a lot of defaults. In the game I have, the transistors were 8050 and 8055 (I don't know about the LED), but most posts I've read suggested that the exact values for the parameters shouldn't matter.

Does anyone know:

1. How to estimate the oscillation frequency? (that is, without building the circuit and doing measurements, hopefully using only pen and paper, if possible)

2. Why is it oscillating? (I tried a very simplistic analysis, using the linear approximation of the transistor equations, but -maybe a made a mistake? - the capacitor C2 seems to be charging all the time)

3. Why aren't the simulators showing any oscillation? Are their models too simplistic? Does it only oscillate for very specific transistors/diode?

^{simulate this circuit – Schematic created using CircuitLab}

Answer 1

Besides G36's suggestions for answers, here's an LTspice attempt, not using uic, or startup, or a pulsed supply, or ic:

It's a simulation ran with both a 100n and a 100\$\mu\$ cap in parallel with the 5k1 resistor, to see the effects of it. Also, I left the schematic as you showed it, but you need some sort of resistor in series with the LED, the spikes (even though short lived) from the supply are well over 0.5A.