I made the assembly here attached (01-diagram Montage).
So far so good.
My program loaded on the ESP32 activates, every 5 seconds the PIN GPIO17 which sends 3.3V.
The led flashes nicely.
If I replace (between 1 and 2) the LED and its resistance by my motor (12V 0.07A) nothing happens.
if I plug my engine between the + 12V and the pin Source of the IRF3708 the engine runs.
I find myself facing a mystery that goes far beyond my knowledge in electronics.
Forum experts will certainly give me tracks to run my engine.
That MOSFET just barely opens at 3.3V. Get yourself a logic level one that actually fully opens at 3.3V - but it's going to be hard to find one in convenient TO220 or even TO92 package. The ones that I use are SOT-23 packages.
Your LED needs very little current: it will glow with your MOSFET a little open.
Your motor needs a lot of current: you need to properly open the MOSFET to make it work, so for your MOSFET you need 10V or more on the gate. You could use the 12V of your power supply with appropriate driver circuit for the MOSFET you have.
That's getting confusing - IRF devices that have logic level gates. It's supposed to be an IRL number then. Indeed based on the data sheet it should work just fine at 5V.