Hi Ken,
My thoughts are with you and with your second cousin's family. Death by suicide is hard for family and friends to bear under any circumstances and your question about its incidence among the witnesses is a good one. To the best of my knowledge no rigorous, scientific study on the incidence of suicide among the witnesses has ever been done. Some observers have speculated about the incidence of mental illness among the witnesses, but it is important to stress these are speculative and not good examples of well-designed studies. Unfortunately, Jerry Bergman's "work" on the topic of mental illness among the witnesses is deeply flawed and he lets his hunches run away with him. He speaks in terms of comparative percentages of mental illness among the witnesses compared with the general population. Moreover, his thesis is simplistic; namely, that the Watchtower teachings "cause" mental illness. There are other hypotheses that could be equally plausible such as these 2:
1. troubled people are morel likely than others to be attracted to the Watchtower's teachings so they "bring" their mental-health problems with them into the religion.
2. the witnesses, as a marginalised and misunderstood group are more likely than others to be subjected to stress and hence more likely to experience mental health problems.
I must say that, in my opinion, there is no compelling evidence that witnesses suffer higher than "normal" rates of mental illness than non-witnesses. This does not minimise the seriousness of these problems. Anyone prone to mental health problems, especially if it is accompanied by suicidal thoughts, needs to be taken seriously and given good quality help. Those with suicidal thoughts can be helped to address the problems that have led them to feel that way and develop more helpful ways of coping.
Take care.