The Nayanars were leaders who were devoted to Shiva. They were part of a group of Tamil poet-saints who lived between the 5th and 10th centuries in South India. The Nayanars were known for their intense devotion, mystical experiences, and fervent worship of Lord Shiva. They composed numerous devotional hymns and poems in praise of Shiva, which are collectively known as Thevaram.

Option 1, which states that the Nayanars were immersed in devotion to Vishnu, is incorrect. The Nayanars were specifically devoted to Lord Shiva and not Vishnu.

Option 2, which suggests that the Nayanars were devotees of Buddha, is also incorrect. The Nayanars were not followers of Buddha but were dedicated to Shiva.

Option 4, which claims that the Nayanars were devotees of Basveshwara, is also incorrect. Basveshwara was a 12th-century social reformer and religious leader in Karnataka, India. The Nayanars lived several centuries before Basveshwara and were not associated with him.

Therefore, the correct answer is option 3, stating that the Nayanars were leaders who were devotees of Shiva.