We measure the signal of secondary halo bias as a function of a variety of intrinsic and environmental halo properties, and characterize its statistical significance as a function of cosmological redshift. Using fixed and paired $N$-body simulations of dark-matter halos -- the UNIT simulation -- with masses above $10^{11}M_{\odot}h^{-1}$ identified over a wide range of cosmological redshifts (0<z<5), we explore the behavior of the scaling relations among different halo properties. We include novel environmental properties based on the halo distribution as well as the underlying dark-matter field. We implement an object-by-object estimator of large-scale effective bias and test its validity against standard approaches. With a bias assigned to each tracer, we perform a statistical analysis aiming at characterizing the distribution of bias and the signal of secondary halo bias. We show how the halo scaling relations linking direct probes of the halo potential well do not depend on the environment. On the contrary, links between halo mass and the so called set of secondary halo properties are sensitive to the cosmological environment. We show that the signal of secondary bias derives statistically from secondary correlations beyond the standard link to halo mass. We also show that the secondary bias arise through non-local and/or environmental properties related either to the halo distribution or to the properties of the underlying dark-matter field. Properties such as the tidal field and the local Mach number generates the signals of secondary bias with the highest significance. We propose applications of the assignment of individual bias for the generation of mock catalogs containing the signal of secondary bias, as well as a series of cosmological analyses aiming at mining large galaxy data sets.