I've corrected this answer now, thanks to the comment from Tyler Lawson.
Let me use $B_n$ for the finite Boolean lattice of subsets of $[n] := \{1,2,\ldots,n\}$ (your $\mathcal{P}(S)$), and let $k=|T|$. Then your $A=((B_k\setminus \{\hat{1}\}) \times B_{n-k}) \setminus \{\hat{0}\}$, where $\hat{0}$ means the minimum of a poset, and $\hat{1}$ the maximum. To understand the homotopy type of this product, we need a result of Quillen (stated as Theorem 5.1(b) in the paper "Canonical homeomorphisms of posets" by Walker cited below; see also the discussion in Section 5.1 of the notes of Wachs), which says that $$ |P\times Q \setminus \{\hat{0}\}| \simeq |P\setminus \{\hat{0}\}| \ast |Q\setminus\{\hat{0}\}|,$$ for posets $P,Q$ which have minimums, where $\ast$ is the join of complexes. So in our case $$ |A| \simeq |B_k \setminus \{\hat{0},\hat{1}\}| \ast |B_{n-k}\setminus \{\hat{0}\}|.$$ But $B_{n-k}\setminus \{\hat{0}\}$ is contractible (it has a maximum), so $|A| \simeq |B_k \setminus \{\hat{0},\hat{1}\}| \simeq \mathbb{S}^{k-2}$, as you guessed.
Quillen, Daniel, Homotopy properties of the poset of nontrivial p-subgroups of a group, Adv. Math. 28, 101-128 (1978). ZBL0388.55007.
Wachs, Michelle L., Poset topology: tools and applications, Miller, Ezra (ed.) et al., Geometric combinatorics. Providence, RI: American Mathematical Society (AMS); Princeton, NJ: Institute for Advanced Studies (ISBN 978-0-8218-3736-8/hbk). IAS/Park City Mathematics Series 13, 497-615 (2007). ZBL1135.06001.
Walker, James W., Canonical homeomorphisms of posets, Eur. J. Comb. 9, No. 2, 97-107 (1988). ZBL0661.06006.