Talking about suicide is not at all the same as suicidal ideation.

Talking about suicide implies thoughts about suicide, and the definition of suicidal ideation Vaniver quoted says such thoughts demonstrate suicidal ideation. If so, talking about suicide implies suicidal ideation.

There are narrower definitions of suicidal ideation (e.g. the two you cited earlier) but I worry that broad definitions like Wikipedia's prime people to interpret discussion about suicide in general as a reliable sign of suicidal ideation or being mentally unbalanced. jooyous might have a similar concern.

(I'm not saying you're doing that in this case. Someone mentally simulating suicide on an ongoing basis clearly is engaging in suicidal ideation.)