I live in Florida and talk to my T about suicidal thoughts. We talk about it: how did the thoughts begin, what was going on, etc. Of course she is also evaluating my present state of mind.

I am lucky that another T told me once that suicidal thoughts are a way of saying how much pain a person is in; *this much* pain. Lucky because I can think of that and be reminded that it is pain that seems to have nowhere to go, that needs someone to listen to it, someone to comfort it.
It nees ME to express it so it can be relieved. My talking about it starts this process of relief. The more I do it, the easier it is to notice the *this much* pain that is there and that needs my attention. The earlier I notice it, the earlier I can start the process of relieving it and so the intensity of the experience is lessened and less dramatic.

My T knew I was borderline before I did. Only after reading on my own did I approach her with the idea that it seemed to apply to me, and she readily agreed and said she'd thought that for some time. The diagnosis isn't a focus of my therapy.
I also decline meds at this time but took them for years.

She is available to me by phone between sessions. She is a LMHC (licenses mental health counselor) and has a Masters and just finished psychoanalytic training. When I looked into the LMHC designation, I liked what I read. Before this T, I thought only a Psychologist could do 'good' therapy. Not so, I found out. This therapy I am in is great.

I have had many other T's but the therapy was not very helpful.
This time I research therapists and therapies to figure out what I wanted.
Here's a site that helped me: www.guidetopsychology.com.
Once I determined that I wanted psychoanalytic/psychodynamic therapy, I contacted the nearest psychoanalytic training institute and asked if they had any candidates who were in practice in my area. (A candidate is an student who is already a therapist, who is highly qualified, and has been screened for admission to the institute. I felt good about choosing someone who had been accepted by the training institute). I was lucky that they had someone to refer me to.

Keep looking and I'm sure you will find a T who can work well with you.
"Trust the process" as my T has told me from day one.