  Luminous red galaxies (LRGs) and blue star-forming emission-line galaxies
(ELGs) are key tracers of large-scale structure used by cosmological surveys.
Theoretical predictions for such data are often done via simplistic models for
the galaxy-halo connection. In this work, we use the large, high-fidelity
hydrodynamical simulation of the MillenniumTNG project (MTNG) to inform a new
phenomenological approach for obtaining an accurate and flexible galaxy-halo
model on small scales. Our aim is to study LRGs and ELGs at two distinct
epochs, $z = 1$ and $z = 0$, and recover their clustering down to very small
scales, $r \sim 0.1 \ {\rm Mpc}/h$, i.e. the one-halo regime, while a companion
paper extends this to a two-halo model for larger distances. The occupation
statistics of ELGs in MTNG inform us that: (1) the satellite occupations
exhibit a slightly super-Poisson distribution, contrary to commonly made
assumptions, and (2) that haloes containing at least one ELG satellite are
twice as likely to host a central ELG. We propose simple recipes for modeling
these effects, each of which calls for the addition of a single free parameter
to simpler halo occupation models. To construct a reliable satellite population
model, we explore the LRG and ELG satellite radial and velocity distributions
and compare them with those of subhalos and particles in the simulation. We
find that ELGs are anisotropically distributed within halos, which together
with our occupation results provides strong evidence for cooperative galaxy
formation (manifesting itself as one-halo galaxy conformity); i.e.~galaxies
with similar properties form in close proximity to each other. Our refined
galaxy-halo model represents a useful improvement of commonly used analysis
tools and thus can be of help to increase the constraining power of large-scale
structure surveys.
