Possible interpretation for points of non equilibrium in a 2D ODE system where only one of the components of the vector field is $=0$.

Question

I have a 2D ODE system $$ x'=F(x), $$ where $x=(x_1,x_2)$, i.e., $$ \begin{cases}x_1'(t)=F_1(x)\\ x_2'(t)=F_2(x);\end{cases} $$ A component of the vector field $F$ I have vanishes at a point $x=(x_1,x_2)$, i.e. $F_2(x)=0$. If $F_1(x)=0$, then $x$ would be an equilibrium point. However, I only have $F_2(x)=0$: can I still get some substantial information about the behavior of the solution $$ x(t)=\big(x_1(t), x_2(t)\big) $$ around such points of $F(x)$?

Many thanks.