In the realm of nuclear safeguards, passive neutron multiplicity counting using shift register pulse train analysis to nondestructively quantify Pu in product materials is a familiar and widely applied technique. The approach most commonly taken is to construct a neutron detector consisting of 3He filled cylindrical proportional counters embedded in a high density polyethylene moderator. Fast neutrons from the item enter the moderator and are quickly slowed down, on timescales of the order of 1-2 [mu]s, creating a thermal population which then persists typically for several 10's [mu]s and is sampled by the 3He detectors. Because the initial transient is of comparatively short duration it has been traditional to treat it as instantaneous and furthermore to approximate the subsequent capture time distribution as exponential in shape. With these approximations simple expressions for the various Gate Utilization Factors (GUFs) can be obtained. These factors represent the proportion of time correlated events i.e. Doubles and Triples signal present in the pulse train that is detected by the coincidence gate structure chosen (predelay and gate width settings of the multiplicity shift register). More complicated expressions can be derived by generalizing the capture time distribution to multiple time components or harmonics typically present in real systems. When it comes to applying passive neutron multiplicity methods to extremely intense (i.e. high emission rate and highly multiplying) neutron sources there is a drive to use detector types with very fast response characteristics in order to cope with the high rates. In addition to short pulse width, detectors with a short capture time profile are also desirable so that a short coincidence gate width can be set in order to reduce the chance or Accidental coincidence signal. In extreme cases, such as might be realized using boron loaded scintillators, the dieaway time may be so short that the build-up (thermalization transient) within the detector cannot be ignored. Another example where signal build-up might be observed is when a 3He based system is used to track the evolution of the time correlated signal created by a higher multiplying item within a reflective configuration such as the measurement of a spent fuel assembly. In this work we develop expressions for the GUFs which include signal build-up.