I finally found the picture or the schematic I drew. (And roughly simulated) It's attached.
The resistor in the picture is where the pot is. Also there is a second transistor in parallel with the one in the picture. This one is a different type and it's glued with thermal paste to the one in the schematic. I'm not sure if the paste was necessary, but I figured, since they sit flat-face to flat-face (ones pins are mirrored since diff. type) on the board, I might as well couple them thermally.
I can't connect anything directly to the LED. It would probably stop oscillation. So it has to be in place of the resistor.
I assume I also can't use the Batteroo or Batterizer. I guess they don't put out flat DC and would interfere, or they just ruin the efficiency. But I'll see where I can get one.
@JS does it even matter if it is P or N channel? I take a look around, but the Ig Vgs or Vds plots are with negative current. Does that matter? Why is it negative?
@mmagin Hm. Oh: "The circuit generates constant current pulses" nope, not gonna work, I think. (How is that constant xD)
I'll try to find a JFET and one of these batterizeroos if they don't cost too much.
Thank you very much so far
If you have more ideas now that you have the schematic, please tell me.