Ingress to Ingress?

I’m following these instructions Basic Authentication - NGINX Ingress Controller to add basic auth to an NGINX Ingress. This is in EKS. I already have an ALB Ingress which does route to our Service. I had hoped I could insert an NGINX Ingress between the two. However, trying to point the ALB Ingress at the NGINX Ingress causes Kubernetes to complain that there is no such Service. This does make some sense as an Ingress is not a Service, I think. For example:

apiVersion: networking.k8s.io/v1
kind: Ingress
metadata:
  name: foobar-ingress-dev
  namespace: foobar-dev
  annotations:
    kubernetes.io/ingress.class: alb
    alb.ingress.kubernetes.io/group.name: foobar-ingress-dev
    alb.ingress.kubernetes.io/scheme: internal
    alb.ingress.kubernetes.io/target-type: ip
    alb.ingress.kubernetes.io/listen-ports: '[{"HTTP":80}, {"HTTPS":443}]'
    alb.ingress.kubernetes.io/healthcheck-path: /
    alb.ingress.kubernetes.io/backend-protocol: HTTP
    alb.ingress.kubernetes.io/healthcheck-protocol: HTTP
    alb.ingress.kubernetes.io/actions.ssl-redirect: '{"Type": "redirect", "RedirectConfig": { "Protocol": "HTTPS", "Port": "443", "StatusCode": "HTTP_301"}}'
spec:
  tls:
    - hosts:
        - foobar.example.com
  rules:
    - host: foobar.example.com
      http:
        paths:
          - pathType: Prefix
            path: /
            backend:
              service:
                name: ssl-redirect
                port:
                  name: use-annotation
          - pathType: Prefix
            path: /
            backend:
              service:
                name: foobar-ingress-basic-auth-dev
                port:
                  number: 3000
---
apiVersion: networking.k8s.io/v1
kind: Ingress
metadata:
  name: foobar-ingress-basic-auth-dev
  namespace: foobar-dev
  annotations:
    kubernetes.io/ingress.class: nginx
    nginx.ingress.kubernetes.io/group.name: foobar-ingress-basic-auth-dev
    nginx.ingress.kubernetes.io/scheme: internal
    nginx.ingress.kubernetes.io/auth-type: basic
    nginx.ingress.kubernetes.io/auth-secret: foobar-basic-auth-secret-dev
    nginx.ingress.kubernetes.io/auth-realm: 'Authentication Required'
spec:
  defaultBackend:
    service:
      name: foobar-dev
      port:
        number: 3000

Is this possible? Or is there a better way to add basic auth like this? Thanks

Cluster information:

Kubernetes version: v1.21.14-eks-18ef993
Cloud being used: AWS
Installation method: EKS