...as I’m counting he takes over the control and opts to put himself in time out...

There's nothing wrong in that that I can see. If the child feels better having a bit of control over this, fine! As long as they do the time out. "Negotiating" a time out implies, to me, that they start trying to get out of doing a time out or change it in some way ("I'll sit down here and be quiet!") by pleading or arguing, and the whole point of counting is to stop engaging in conflict. Your child taking himself to a timer out voluntarily is not prolonging conflict.

Regarding anxiety, there's no law stating that a time out needs to be in a room where the child is alone and frightened. Sure, most parents choose the child's bedroom, but it could be a corner of the room you're in, or the next room over from where you will be, whatever. The point is to have quiet time to gather oneself up again and settle down.

If you're the child's primary caretaker, you know them better than anyone else. If their anxiety is real, then adjust your consequences and expectations. For an extremely anxious child, sitting quietly in the corner for the prescribed time may be all they need as a consequence of getting to "3". If they speak, the timer is reset from the beginning or by a certain amount (you need to be the judge of whether they are gaming the system.)

All of this must be discussed and expectations need to be outlined (and, I would add, allowing and considering/respecting the child's feedback) ahead of time, when all is well and peaceful. There needs to be understanding of the system and, to some degree, agreement, even if it's only that time outs are better than x alternative (taking away a toy, an activity, or other often unhelpful "consequence"). After the time out, there needs to be some discussion and reflection. It doesn't need to be a long, drawn-out affair, but it needs to happen most of the time ("Can you tell me why you had a time out? Do you think you can make better choices?" And every once in a while, "Is there a different way we can help you make better choices?".)

I guess the take home message is that 123 Magic is a style, not a rule book. If you agree with the style, adjust the rules to fit your particular situation while keeping within the principles. And feel free to ask questions!

...as I’m counting he takes over the control and opts to put himself in time out...

There's nothing wrong in that that I can see. If the child feels better having a bit of control over this, fine! As long as they do the time out. "Negotiating" a time out implies, to me, that they start trying to get out of doing a time out or change it in some way ("I'll sit down here and be quiet!") by pleading or arguing, and the whole point of counting is to stop engaging in conflict. Your child taking himself to a time out voluntarily is not prolonging conflict. However, trying to negotiate where he will have the time out isn't ok. Maybe at the beginning of a period of time (say a week), you can come to an agreement about where a time out will take place, giving the child a feeling of some control? From that agreement on, for that period of time, it's non-negotiable. ("We agreed on this already. That's a two..." and discuss after the time out. Integrity isn't learned when we change our agreements all the time.)

Regarding anxiety, there's no law stating that a time out needs to be in a room where the child is alone and frightened. Sure, most parents choose the child's bedroom, but it could be a corner of the room you're in, or the next room over from where you will be, whatever. The point is to have quiet time to gather oneself up again and settle down.

If you're the child's primary caretaker, you know them better than anyone else. If their anxiety is real, then adjust your consequences and expectations. For an extremely anxious child, sitting quietly in the corner for the prescribed time may be all they need as a consequence of getting to "3". If they speak, the timer is reset from the beginning or by a certain amount (you need to be the judge of whether they are gaming the system.)

All of this must be discussed and expectations need to be outlined (and, I would add, allowing and considering/respecting the child's feedback) ahead of time, when all is well and peaceful. There needs to be understanding of the system and, to some degree, agreement, even if it's only that time outs are better than x alternative (taking away a toy, an activity, or other often unhelpful "consequence"). After the time out, there needs to be some discussion and reflection. It doesn't need to be a long, drawn-out affair, but it needs to happen most of the time ("Can you tell me why you had a time out? Do you think you can make better choices?" And every once in a while, "Is there a different way we can help you make better choices?".)

I guess the take home message is that 123 Magic is a style, not a rule book. If you agree with the style, adjust the rules to fit your particular situation while keeping within the principles. And feel free to ask questions!