Achieving fault tolerance with superconducting quantum processors requires qubits to operate within the regime of threshold theorems based on the Born-Markov approximation. This approximation, which models dissipation as constant energy decay into a memoryless environment, breaks down when qubits couple to long-lived two-level systems (TLSs) that become polarized during operation and retain memory of past qubit states. Here, we show that non-Poissonian quantum jump traces carry the information required to distinguish long-lived TLSs from the standard Markovian bath. By fitting the Solomon equations to measured quantum jump dynamics arising naturally from thermal fluctuations, we can disentangle the qubit’s coupling to the two environments. Sweeping the qubit frequency reveals distinct peaks, each associated with a TLS that outlives the qubit, providing a handle to understand their microscopic origin.