I-surfaces with one T-singularity

We classify normal stable surfaces with $K_X^2=1$, $p_g=2$ and $q=0$ with a unique singular point which is a non-canonical T-singularity, thus exhibiting two divisors in the main component and a new irreducible component of the moduli space of stable surfaces ${\overline{\text{gothM}}}_{1,3}$.