In the first installment of this series, we proved that for every integer \(a \geq 3\) and every \(m \geq 2a^2 – a + 2\), the \(2\)-color Rado number of \[x_1+x_2+\ldots+x_{m-1}=ax_m\]. is \(\lceil \frac{m-1}{a} \lceil \frac{m-1}{a} \rceil\rceil \). Here, we obtain the best possible improvement of the bound on \(m\). Specifically, we prove that if \(3|a\), then the \(2\)-color Rado number is \(\lceil \frac{m-1}{a} \lceil\frac{m-1}{a} \rceil\rceil \) when \(m \geq 2a + 2\) but not when \(m = 2a+1\), and that if \(3 \nmid\) is composite, then the \(2\)-color Rado number is \(\lceil \frac{m-1}{a}\lceil\frac{m-1}{a}\rceil \rceil \) when \(m \geq 2a + 2\) but not when \(m = 2a + 1\). Additionally, we determine the \(2\)-color Rado number for all \(a \geq 3\) and \(m \geq \frac{a}{3} + 1\).