Setup vault agent injector auth path globaly

Hi,
I need help with some configurations
I have many K8S clusters and I want to connect them to my central Vault cluster.
After agent injector deployment on K8S cluster and setup it and everything is ok.
The problem is when I configure kubernetes access.
Default auth path for agent injector is auth/kubernetes.
The problem when we want to setup authentication from multiple clusters like:
cluster1
cluster2
cluster3
on different auth path for example: auth/cluster1 etc.
The agent default auth path is always set to auth/kubernetes so even if I set authenthication correctly for path auth/cluster1 I get permission denied error from init container:

URL: PUT https://vault.example.com:8200/v1/auth/kubernetes/login

because agent use default auth path.

After some research I found I can add annotation to pod:
vault.hashicorp.com/auth-path: '/auth/cluster1'

but I’m looking a option to set it globaly for whole k8s cluster.