Component template

How to reference the custom analyzer present in settings component template in mappings component template?

I have created a component template for settings as shown below but creating a mappings component template that references customer analyzer defined in settings component template failing with error

{
  "error": {
    "root_cause": [
      {
        "type": "mapper_parsing_exception",
        "reason": "Failed to parse mapping [_doc]: analyzer [my_custom_analyzer] has not been configured in mappings"
      }
    ],
    "type": "mapper_parsing_exception",
    "reason": "Failed to parse mapping [_doc]: analyzer [my_custom_analyzer] has not been configured in mappings",
    "caused_by": {
      "type": "illegal_argument_exception",
      "reason": "analyzer [my_custom_analyzer] has not been configured in mappings"
    }
  },
  "status": 400
}

Why it is not working? Any idea?
btw i am using ES version 7.17.20

PUT _component_template/settings_template
{
  "template": {
    "settings": {
      "analysis": {
        "filter": {
          "my_custom_filter": {
            "type": "synonym",
            "synonyms": [
              "quick,fast",
              "jumps,leaps"
            ]
          }
        },
        "analyzer": {
          "my_custom_analyzer": {
            "type": "custom",
            "tokenizer": "standard",
            "filter": [
              "lowercase",
              "my_custom_filter"
            ]
          }
        }
      }
    }
  }
}

PUT /_component_template/mappings_template
{
  "template": {
    "mappings": {
      "properties": {
        "content": {
          "type": "text",
          "analyzer": "my_custom_analyzer"
        }
      }
    }
  }
}

Each component template is independent from the others. It means that you must set the analyzer within the same component template where you will use it.

thanks much David. From the examples thought we can do so.

What happens when two component templates having same analyzer are part of a composable template? Which analyzer will be considered?