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.
