As any counseling character soon discovers, you don't get many patients at your door. Few people are willing to subject their characters to the type of flaw required to need counseling.
Therefore, it's a common tendency to try and find patients. This is rarely a good idea. Pouncing on every crewman who seems to be having a bad day borders on harassment. If others resent your character being a busy body, you've reduced your chances even further of having any significant interaction with them.
However, by simply paying attention to the happenings aboard ship, a person playing a counselor will find plenty of opportunities to get involved without cornering their crewmates. It is a matter of recognizing where counselor intervention is required.
The death of a crewman or a member of his family deserves counselor attention; usually in the form of a sympathetic ear for the bereaved. A counselor is also a logical contributor to any interrogation process to provide insight into body language and motivations. Likewise, a counselor should be included on diplomatic missions or other cultural exchanges. Characters who attempt suicide or exhibit other extreme irrational and/or dangerous behavior, require serious psychological attention. And it is in these cases that the counselor is both expected and required to force interaction.
Common sense on the part of the player is necessary in handling any counseling situation. Remember, a counselor should be viewed as an asset to the crew, not an annoyance.