Andrews–Bachraoui conjecture on the values of $b_2''(n)$

Let $b_2”(n)$ be the signed count associated with partitions whose parts greater than $1$ lie in $[2k,2l-1]$, whose smallest even part is $2k$, whose number of ones is $l-1$, and whose odd parts greater than $1$ are distinct; each partition with $j$ parts greater than $1$ has weight $(-1)^{j+1}$. Andrews–Bachraoui conjecture. For any positive integer $n$,

$$b_2”(n)\in\{-1,0,1,2\}.$$

This is the range assertion identified in the source as the original second conjecture. No resolution is supplied in the given text.