When my suicidal thoughts were constant, my therapist and I worked to help me figure out when they were "just thoughts" versus when there was intent and/or a plan attached. This was helpful because the person prescribing my meds was totally freaked out by the suicidal thoughts (my therapist recognized them as a sort of 'coping mechanism'). He then told me that it was possible I would always have them - which for some reason "clicked" with me and made me able to accept them as thoughts and I was able to let them drift along in my head without reacting to them. I was then able to see that they were reactions to triggers - even non-trauma-related triggers, like being overly tired or overwhelmed with work or the kids.
Recently (the past two months or so), I've been able to gently respond to them when they come up - I acknowledge them, let them know that I understand that things are overwhelming, and then telling them that "suicide is not an option". I can then ask myself what would help me feel better just for that moment (I think this is basically "distress tolerance").
It's taken a while to reach the point where I can quiet them down pretty quickly. I think by using the acceptance, self-talk and distress tolerance, I've been able to "shift" the way my brain works.