Hello everyone, sorry for the delay in replying, I did it!
I disassembled the wire bundle, the neutral goes to the main coil and the phase goes to the two wires of the "secondary" or starter coil, as you call it.
The capacitor receives the phase and sends it to one of the two wires of the secondary coil, then the output of the capacitor, connected to wire 1 secondary coil goes in one direction, to wire two secondary coil goes in the other.
I hope I am not confused, I made the change days ago, I made a horrible little drawing,
I hope it is clear.
(I cut, welded, modified the length of the cables, and tied the cables just to keep them from moving, without putting everything back exactly in the original position, but thrown them at random, and doing the job without particular attention, I used a normal shrinking sheath , the motor works great in both directions, so don't worry too much, only caution, do not scratch / damage the copper wires of the winding, I have soldered and cut on the original soldering of the wires and I have cut the wires after soldering, not I "handled" the copper wires of the windings)I ordered on amazon 2 sewing machine pedals, I spent 8 €,
When I press pedal 1, the phase reaches auxiliary wire 1, when I press pedal 2, the phase reaches auxiliary wire 2.
the pedals have 3 poles, com, normally open, and normally closed,
The phase arrives at the com of pedal 1, it leaves the normally closed of pedal 1 entering the com of pedal 2, so when pedal 1 is pressed, the phase goes to the motor and is excluded by pedal 2.
if both pedals are accidentally pressed, pedal 2 is excluded and the motor proceeds in the normal running direction, and phase from both pedals will never arrive at the same time.
The start was obviously 100% immediate, impossible to fillet without destroying the taps, so I bought a 220V voltage regulator (€ 9) to regulate the speed.
I also added a switch to disconnect the phase to the drill, so we avoid accidental switching on the pedals.
The only flaw is that the speed regulator works, but if you adjust it to make it run slowly, the engine has very little power, so you have to adjust it a little faster than you need and dose the pressure time carefully, but I like it this way it also works as a soft starter as well.
It's not the best, but for 17 € I'd say it's great.
I have a lot of stepper motors that I replaced on my 4 axis CNC some time ago, later I build a well done bench threader.
Thank you all for the support !
I uploaded a video
(for indexing)
How to reverse direction motor monophase, economical column drill.