In Jain practice, head-covering is not a universal scriptural rule for all followers. It is mainly a local custom (maryāda) followed by many Śvetāmbara communities and some temples to show modesty and respect during puja, pratikraman, and darshan. It is often encouraged for women, but it is not required for men by Jain scriptures themselves. ( jainknowledge.com)

Key points:

• Why women cover the head: In many temple settings, women cover the head as a sign of respect and modesty during religious activities. It is a community practice, not a firm scriptural mandate. ( jainknowledge.com)
• Is it required for men? No universal rule mandates men to cover the head. Dress norms emphasize cleanliness, simplicity, and reverence, but head-covering for men is not a core requirement in Jain scriptures. ( jainknowledge.com)
• Digambar vs Śvetāmbara: Śvetāmbara communities more commonly observe head-covering for women as part of local maryādā; Digambar communities have their own distinct practices, and head-covering for women is not a universally fixed rule across all Digambar temples. The essential Jain focus remains on shuddha bhav and proper conduct rather than clothing alone. ( jainknowledge.com)

If you want, I can point you to specific temple maryādas or dress norms for your local sangh. You can read more about modest dress norms for shravakas here and about whether head-covering is advised in practice here .