I can only describe my own experience as management grade union rep in the rail industry for 20+ years.
I attended many formal meetings with individuals who were not union members. But made it clear to the individual and management side that I was attending in the capacity of a “colleague” not a union rep. I always asked for that to be minuted and noted by the chair of any formal meeting.
I did so, because most people in dispute with the employer (discipline, poor performance, whatever), are not in a good place, and needed an ear to help them process what was happening. They needed a critical friend, who could help explain the process, listen to the management case, and repackage that up and reflect it back to help the employee to see where they were. How to respond and to think through their options. I never gave formal advice to Non union members. instead I was always told them to look up information on both the ACAS and Citizens Advice websites to check that my informal advice was in line with employment law. Only union members (with the length of membership that gave them), access to full time officers and the legal advice would receive formal support. That after all is what they paid for.
For me this was both about supporting a colleague in distress, but it also helped other colleagues and management. Because management knew the employee was having support from an informed colleague. Having an employee in dispute, supported by an informed colleague, made the process quicker. And IMHO the outcomes fairer. for example, it meant managers were less likely to try to push the boundaries of the company process. This ultimately was to the benefit of all employees including the union members.
A good staff rep ensures that the formal process of representation and negotiation is undertaken in a cordial and professional way.
Extending that experience to help non union members, ultimately helped build the important trust and professional confidence between union and management. Management knew that an individual was receiving impartial support that helped oil the process. That was good for management and the employee in dispute. This also helped union members as management respected union participation in issues related to terms and conditions, reorganisations and pay.
When BR was a closed shop all individuals were union members and represented by lay and full time union officials. When that changed, non union members could not insist on individual support from lay union and professional union reps.