Do you propose that Training Manager must report to Technical Managers rather than HR?

yes

I do not think so Training Manager repor to Technical Manager or HR Manager. Training is the part of HR for that reason Training Manager can report to the Head of HR but not HR Manager. Manager report to another Manager it should not create total satisfaction of employee or position.

Depending on the depth of course, all three should actually sit on a comittee to determine the needs and to have correct actions to meet the training needs.

It depends on the nature of job hired for and most important is the purpose a person is hired for.

If the organization intends bringing in unskilled pool to train tailor made programs, I would recommend Training manager would have to report to HR

On the other hand, in case of experienced hires what is given in most cases is an orientation and would be an added advantage to the core skill a resource is hired for (based on Technical Managers specs), it makes sense for the trainers to evaluate and share the results with Technical Managers.

In simple words, Pre Process training should fall under HR and In Process (OJT) training should fall under production Managers scope.