Head shaving when father is alive

Question

Elders in community say full shaving of head is not allowed for those with living father (parents). Only at the death of the father the head is full shaved and after that one can shave any time.

Here full head shave I mean without tuft (Shikha). At chudakarma, upanayana or brahmacharya days head is shaved but tuft is left. But clean shave not allowed.

Any references in scriptures why this is not allowed, or any references which prescribes clean head shave at death of parent?

Note: question is not about shaving head at temples like Tirupati (even that is not allowed in my community; we have to keep the tuft). Also, question is not about Chudakarma.

Answer 1

Completely shaving the head is allowed for a student (a person living in the Brahmachari phase of life). So, it is allowed even if the father is alive.

Students may shave their heads completely, wear their hair matted, or keep just the topknot matted.

Gautama Dharmasutras 1.27

OR

Manu 2.219. A (student) may either shave his head, or wear his hair in braids, or braid one lock on the crown of his head; the sun must never set or rise while he (lies asleep) in the village

But, usually the top-knot is told not to be cut because without it a shaven headed person is considered as "naked from the top". So, unfit to perform rituals in such a "naked" state. But, it does not appear to be linked with whether one's father is alive or not.

From Apasthambha for example:

At their death one should also bathe daily for the same period of time; 6 in addition, the mourners should shave themselves completely. 7 Some maintain that students who have returned home should not shave except when they are consecrated for a sacrifice.* 8 A Brahmana, moreover, declares: ‘Empty and uncovered, indeed, is he who is shaven-headed; the topknot is his cover.’ 9 At sacrificial sessions, on the other hand, the topknot is shaved because it is explicitly enjoined.