  With the emergence of very high energy astronomy (VHE; E>100 GeV), new open
questions were presented to astronomers studying the multi-wavelength emission
from blazars. Answers to these open questions, such as the Doppler crisis, and
finding the location of the high-energy activity have eluded us thus far.
Recently, quasi-simultaneous multi-wavelength monitoring programs have shown
considerable success in investigating blazar activity. After the launch of the
Fermi Gamma-ray Space Telescope in 2008, such quasi-simultaneous observations
across the electromagnetic spectrum became possible. In addition, with very
long baseline interferometry (VLBI) observations we can resolve the central
parsec region of active galactic nuclei (AGN) and compare morphological changes
to the gamma-ray activity to study high-energy emitting blazars. To achieve our
goals, we need sensitive, long-term VLBI monitoring of a complete sample of VHE
detected AGN. We performed VLBI observations of TeV-detected AGN and high
likelihood neutrino associations as of December of 2021 with the Long Baseline
Array (LBA) and other southern hemisphere radio telescopes at 2.3 GHz. In this
paper we present first light TANAMI S-band images, focusing on the TeV-detected
sub-sample of the full TANAMI sample. Apart from these very high
energy-detected sources, we also show images of the two flux density
calibrators and two additional sources included in the observations. We study
the redshift, 0.1-100 GeV photon flux and S-band core brightness temperature
distributions of the TeV-detected objects, and find that flat spectrum radio
quasars and low synchrotron peaked sources on average show higher brightness
temperatures than high-synchrotron-peaked BL Lacs. Sources with bright GeV
gamma-ray emission also show higher brightness temperature values than
gamma-low sources.
