Googley, I literally came into this forum hoping that there was a post about just this topic. In many ways, I find myself in a similar position to where you are now. I haven't SI'ed in quite some time (5 or so months), yet there isn't a day that goes by where the thought doesn't pop into my head. Similarly, suicidal thoughts will randomly come too.... for example, I was fishing at this beautiful location with lots of cliffs and waterfalls, and very non-chalently, I thought "gee that would be perfect to jump off of to end everything." Its almost as though I have these half-hazard intentions that linger in the background surrounding SI - or other variants - yet I'm not sure what to do/think of them.

As for your new T, I would pretty much explain what you have already mentioned - that thoughts of SI are still in part in your life, however, you wish only to discuss them when they are at the forefront of what you are struggling with at the time. I don't think there is anything "wrong" with you for feeling this way (though I can see how one might perceive this to be a very bias opinion ), but I would bet there are many other people out there with similar happenings - even if they aren't consciously aware of it.

When in doubt... talk it out with your T.
((((((hugs)))))))
J