If you made the circuit in post#9 correctly, then the only reason for not working is the transistor is wired wrong, or the feedback wires need reversing.

 

If you made the circuit in post#9 correctly, then the only reason for not working is the transistor is wired wrong, or the feedback wires need reversing.

Or possibly the bias might be not quite right. Unlike that "slayer" circuit that depends on enough capacitance between coils to provide feedback.

 

TS's circuit:
1. Coils. L1 - 4 μH - 8 turns of wire dia 1mm wounded on coil L2.
L2 - 3.41 mH - 600 turns of wire dia 0.35 mm on PVC tube dia 50mm.
Self capacitance of L2 is 3.37 pF (C2).
2. Resonant frequency of tank L2, C2+Cparasitic is 747.4 kHz (frequency of HV AC).
3. Transistor D2499 modeled by Q1, D1 and R2.
4. Diode D2 - Schottky, If = 6 A. It can not be LED or simple rectification diode.
5. Capacitor C1 - ceramic, should be connected between emitter Q1 and A of L1 leads.
6. Power supply V1 15 V, 4 A (as minimum).
7. Power, dissipates by transistor Q1 is 5 W (needs not small heatsink).

....
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OK, Danko, that is quite a simulation. And I am incredibly impressed by that 10 microfarad ceramic capacitor. And the collector voltage and base current are awesome indeed. Would it work in the real world, though. But if it works that well in simulation and the TS has built the same circuit, then it should work for the TS, we did see the pictures, and there did seem to be some minor differences.Perhaps the local expert,(brother) can make the physical model work as well as the simulation model.
Or is there some small detail that I have missed?

 

Or is there some small detail that I have missed?

Brothers did half of work:

I tried what you told me with aluminum foil, minus contact, from the power supply goes to the foil size 50x50 cm, but again it does not work.

For feedback capacitor they should glue another foil to 50x50 cm cardboard and place this plate on top of L2.
And, of course, connect top lead of secondary coil to foil.
Height of their coil is 21 cm.
It will exactly 10 pF capacitance between top plate and foil pad, they already made.
https://www.daycounter.com/Calculators/Plate-Capacitor-Calculator.phtml

 

A separate feedback winding, sometimes called a "tickler" is a standard way of providing feedback to make the circuit oscillate, and allow the correct bias levels for the required gain. Looking at the currents in the simulation versus the wiring in that picture I would offer that there is NO WAY a circuit wired like that can work.So that also may contribute to the problem.

 

TS's device is completely wrong:

1. Base and emitter connections are swapped (see photos in post #1)

I measured the current with a measuring instrument that consumes Tesla's tower, but it's a miserable 70mA

2. Circuit consumed 70 mA instead 4.6 mA. It means transistor has leakage (may be already killed).