As Enterprise Architect in an organisation, you don’t have any formal decision power, and you don’t have any P&L responsibilities.
If I business manager doesn’t follow your advise, there is a number of different options:
Formal escalation to a higher level as defined in the process. Best option, but often not availible.
Informal escalation to a higher level, but this may be seen as a very bad move by other stakeholders.
Accept situation, but if consequences are servere, that may be a challange.
Accept that your proposal was technically best, but not working in real life. This is tough.
Find a motivation for the business manager to change opinion and do as you say
The last one is based on the criterias that motivaties the manager to take decusions. Is it financial rewards, hunger for power, fame or something else? When you know his or her motivations, your have the means to pursuade your will.
But when different stakeholders have conflicting agendas, and you want common solution, you have a real problem as shown with #brexit.
In these cases, my recommendation is to have local solutions for each stakeholders, and get all of them to accept this.