Can a non-custodial parent seek visitation rights after the child turns 18?
Technically no, since the child is no longer technically a child once the "child" turns 18.
Of course, you could simply make visitation arrangements directly with the 18-year-old. If he or she wants to be visited, then he or she should be able to make arrangements with you directly.
If there are peculiar circumstances in your case, it may be possible to petition the court for visitation rights of a child over the age of 18, but this would involve an examination of the circumstances.
Mark S. Guralnick