In the book of By-laws written by her--"impelled by a power not one's own"-- there is a paragraph which explains how and when her disciples came to confer a title upon her; and this explanation is followed by a warning as to what will happen to any female Scientist who shall desecrate it: "The title of Mother.

Therefore if a student of Christian Science shall apply this title, either to herself or to others, except as the term for kinship according to the flesh, it shall be regarded by the Church as an indication of disrespect for their Pastor Emeritus, and unfitness to be a member of the Mother-Church." She is the Pastor Emeritus.
While the quoted paragraph about the Procession seems to indicate that Mrs.Eddy is expecting to occupy the First Place in it, that expectation is not definitely avowed.

In an earlier utterance of hers she is clearer--clearer, and does not claim the first place all to herself, but only the half of it.

I quote from Mr.Peabody's book again: "In the Christian Science Journal for April, 1889, when it was her property, and published by her, it was claimed for her, and with her sanction, that she was equal with Jesus, and elaborate effort was made to establish the claim.
"Mrs.Eddy has distinctly authorized the claim in her behalf that she herself was the chosen successor to and equal of Jesus." In her Miscellaneous Writings (using her once favorite "We" for "I") she says that "While we entertain decided views...

and shall express them as duty demands, we shall claim no especial gift from our divine origin," etc.
Our divine origin.