Short answer: Yes, you can listen to Bhaktamar’s 19th shloka during your period. In Jain practice, there are guidelines about ritual purity and temple access, but listening to a bhajan or stotra is not considered forbidden because of menstruation. The key points:

• Periods (masik/menstruation) involve certain temple-entry and ritual-touch considerations in some communities. They commonly restrict entering the sanctum or touching sacred texts, but listening to a bhakti recitation or a stotra is generally acceptable.
• There are differences between Digambar and Shwetambar traditions on details of purity rules. If you follow a specific guru or community, defer to their guidance.
• If your goal is to improve focus, confidence, or job prospects, you can continue with your regular job search and use the recitation as a mental support or moral boost.

If you’d like, I can provide the exact meaning of Bhaktamar’s 19th shloka (arth) from authentic Jain sources, or help you with how different sects interpret it.