Recently I was asked to give advice on how to decide the author position in a list of coauthors. Without knowing nay details of the authors, paper, subject or publisher, I gave the following the general advice. Other members of our network might have different ideas about this. Please tell us!
1. A lot depends on the conventions or rules of a particular discipline or journal.
In the natural sciences, it is common for the most senior author to be last if they had a advisory/supervisory role in the research, but not an active role in writing of the paper.
This last position is not considered 'low' - it is a respected position.
In the case of very large co-author lists, the authors after first author are sometimes listed alphabetically, if a Roman alphabet is being used.
Many journals now request that a statement be given at the end of a paper, after the "Acknowledgments" section, indicating "Author contributions", and these can include many different contributions, not just the analysis or writing. Sometimes the person providing supervision and financial support will be mentioned in the "Acknowledgments section", or sometimes in the "Author contributions" statement.
The "Author contributions" statement is common for the high-impact international journals, and those journal may clearly define the different kinds of contribution that are accepted for co-authors to be recognised as co-authors.
2. Unfortunately, for many local publications, the journal editors and publisher have not discussed what advice to give authors. So it is good for authors to ask for advice from the editors of the journal they submit to, as it will encourage the editors to provide guidance for all authors.
When the journals allow or request an authors contributions statement, then the particular order of the coauthors becomes less important because clear information on contribution is explicitly stated at the end of the paper.
3. Without a clear Author contributions statement, the actual meaning of coauthor position will always be uncertain, since there is no single set of rules for listing coauthors. In your case, perhaps letting the senior coauthor choose their own position is the best option. How readers interpret that position is likely to vary according to the perceptions of each reader.
4. When journals allow a comprehensive "Acknowledgements" section to be included, the pressure to include all contributors as "co-authors" becomes less, and this is better for future use of the paper.
Papers with very long author lists tend to be cited less frequently... or if they are cited, the co-author names are omitted in the bibliography (reference list).
As a reader and writer, I always appreciate it when a journal actively requests an "Acknowledgements" section as well as an "Author contributions" statement.