I do not know of psych positions where one works alone. I worked in psych as a CM and I have never come across an "alone" job. Psych CMs have to work with psychiatric teams. So, there is no alone work. However, case management in general requires autonomy and so in psych or outside of psych you can work independently. Is that what you mean?
I have worked in the field as a psych case manager, where you can independently perform home visits and (if you work with kids) school visits. You are "alone" in your car when you drive to these places, but again, you are driving to connect with a team of people supporting your consumer/client. Maybe that is what you mean? If so, the best way to find one of these positions is to look for positions that are attached to sub acute and community mental health psych facilities with wrap around teams. In addition, having a clinical psych background will be a big plus, but you may need to revamp your resume to reflect your skill set that emphasizes your ability to be flexible within multiple settings, autonomous, able to work in a fast pace ever changing environment, and a team player. Further, if you have not already done so, join the local American Psychiatric Nurses Association to network and show your commitment to this field and specialty .... You never know, you may meet your next manager at a meeting? Good luck!