  Scaling aspects of Gaussian topological phase-transitions in quantum spin
chains are investigated using the prototypical one-dimensional spin-1 XXZ
Heisenberg model with uniaxial single-ion anisotropy $D$. This model presents a
critical line separating the gaped Haldane and large-$D$ phases, with the
relevant energy gap closing at the transition point. We show that a proper
tangential finite-size scaling analysis is able to accurately locate the
Gaussian critical line and to probe the continuously varying set of correlation
length critical exponents. The specific features of the tangential scaling are
highlighted in contrast with the standard scaling holding in the Ising-like
transition between the gapless AF-N\'eel and gaped Haldane phases. Our results
are compared with field-theoretic predictions and available high-accuracy data
for specific points along the Gaussian line.
