Nimitta (external cause) and Ayushya Karma (life-duration karma) are two parts of Jain karma theory that work together to shape our experiences, including how long we live.

• What is nimitta? Nimitta is a catalyst or triggering factor. It can be external (people, objects, events) or internal (aspects of karma itself or mental factors) that helps or guides the manifestation of karmic results. It is not the sole doer, but it helps bring a result into fruition. ( jaincosmos.blogspot.com, jainsite.com, jainworld.jainworld.com)

• What is Ayushya Karma? Ayushya Karma is the specific type of karma that governs the duration of life (how long a life will last). It is one of the karmas that binds to the soul and determines lifespan, though its fruits can be tempered by other factors and the soul’s own purushartha (effort). ( jainknowledge.com)

• How they relate: In Jain thought there are five samavaya (causal relations) that tie actions, karmas, and results together: time (kaal), purushartha (effort), nimitta (external/internal causes), upadan (nishchaya—substrate), and swabhava (nature). Nimitta interacts with Ayushya Karma within this framework: while Ayushya sets the potential duration of life, nimitta can influence when, how, or under what circumstances the karmic results become evident. In other words, nimitta acts as a catalyst or context that can shape the experience of the life-duration karma without changing the essential duration fixed by Ayushya. ( jainsite.com, jaincosmos.blogspot.com)

• Important note for tradition: Jain texts describe nimitta and ayushya within the same system of causation; there can be differences in interpretation between Digambara and Śvetāmbara scholars on details, but the core idea remains that life duration (ayushya) is a karmic fruit that can be modulated in its expression by nimitta and other factors in the fivefold causal framework. ( jainknowledge.com)

If you want, I can point you to a JainKnowledge page that discusses karma theory and the nimitta–upadan–kaal framework in more detail. You can read more here