This is not about what you or I would do but about what a mental health professional would do. I don’t know what I would do in the case of a jumper.....I suspect I would try to persuade them not to jump but not try and forcibly restrain them which is a risky business. People who genuinely want to commit suicide by whatever means will eventually succeed unless confined and closely monitored. Sad but true.
My experience (community work in care of older people) is that people who have an alcohol issue are not sectioned unless its making them dangerously aggressive, a risk to public health, or causing them to steal to support their habit. To be brutally frank, its because there is not a lot of point. Someone who abuses alcohol has to want to get better in order to stand a chance of stopping and, even then, the wanting to stop may not be enough. Someone who is not invested in stopping will find a way to drink if not permanently detained and monitored. My experience is that while its possible, they are maintained in their own homes and when they become too unwell for that, then they move to appropriate care......and believe me I have seen a few, both men, women and couples.
People who deal with the sectioning of adults tend to be pragmatic....One of the things that they will consider is “what would be the point” ie will sectioning and what could be done for the person while under section effect any permanent or even long term improvement in the situation?
In this case I think you will agree that the answer would be no. It won’t help the person concerned, won’t help her family...in fact won’t achieve anything....