The theoretical description of quantum dynamics in an intriguing way does not necessarily imply
the underlying dynamics is indeed intriguing. Here we show how a known very interesting master
equation with an always negative decay rate [eternal non-Markovianity (ENM)] arises from simple
stochastic Schrödinger dynamics (random unitary dynamics). Equivalently, it may be seen as arising
from a mixture of Markov (semi-group) open system dynamics. Both these approaches lead to a more
general family of CPT maps, characterized by a point within a parameter triangle. Our results show
how ENM quantum dynamics can be realised easily in the laboratory. Moreover, we find a quantum
time-continuously measured (quantum trajectory) realisation of the dynamics of the ENM master
equation based on unitary transformations and projective measurements in an extended Hilbert space,
guided by a classical Markov process. Furthermore, a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL)
representation of the dynamics in an extended Hilbert space can be found, with a remarkable property:
there is no dynamics in the ancilla state. Finally, analogous constructions for two qubits extend these
results from non-CP-divisible to non-P-divisible dynamics.