Custom /init script for Target x86?

I need to specify a custom /init script file for a build.
Currently, I am modifying the existing target/linux/generic/other-files/init in order to get my changes included, but I would really prefer to keep it contained in the specific target directory /target/linux/x86 which I am using.
I tried adding the init file in target/linux/x86/base-files/init , but that seems to not be overwriting the /init script of the openwrt build.
Any other ideas to customize the /init script file?