I have two types of suicidal thoughts - one very rational, logical. This would be like what you said about life needing to get better to get rid of the thoughts. Medication won't help me with this except by making my life more manageable.

For whatever reason, my anxiety also manifests itself as suicidal thoughts. This is more of a fixation/intrusive thoughts, and when it gets really bad it's obsessive. Medication helps me with this (benzos) by relieving my anxiety and making the thoughts go away. I deal with this type every day.

It took a long time for me to figure this out.