How to tell if my variable is a suppressor?

I am analyzing data using path analysis and I am hoping someone here can help.

In my model, I am looking at predictors of a variable, $Y$. In the path model, $Y$ has 4 significant predictors lets call them $A$, $B$, $C$, and $X$ (path coefficient $X$ to $Y$ is $-.16$ which is significant). Of importance, $X$ is not significantly correlated with $Y$ when tested as a bivariate correlation ($r = .105$, ns). I feared that suppression may be present and so I ran the partial correlation controlling for $A$, $B$, and $C$. The partial correlation between $X$ and $Y$ was $-.209$, which is significant.

Does this rule out suppression and instead suggest incidental / accidental cancellation may be more likely the issue, or am I missing something? Are there other ways to determine if suppression is the issue?

Simply because the coefficient switched signs and became significant from the bivariate analysis to the multivariate analysis does not guarantee that $X$ is a suppressor. It certainly could be, what you have is the signature effect of suppression, but there are other possibilities as well. For example, $X$ could be confounded with another of the variables in the model, causing the sign to change, but the inclusion of the remaining variables accounts for enough of the residual variance as to make the effect significant. In general, it is hard to ultimately know for sure what the exact relationships are between variables. The best way to determine if $X$ is a suppressor would be to run a new experiment in which you manipulate $X$ and see if there is an effect on $Y$. If it is a suppressor, there will be no effect. (Note that this is an equivalence test, which is more subtle than the prototypical hypothesis testing situation.)