I think it there is no magic rule to do or not a publication bias analysis. However, the lower the number of the studies, the higher is the risk of type II error (lack of power to detect publication bias).

Agreed

I agree with @sebastien. Over the period experience shows that if there are fewer studies(less than 5), your power to detect publication bias is so low that its not recommended. Therefore if the publication journal insists then only you may give otherwise may be avoided