How to query if a time is between two field values

How do I search for documents that are between a start and end time? For example, I want to query the following document using a time only like "18:33" or "21:32". "18:33" would return the following document and "21:32" wouldn't. I don't care about the date part nor the secs.

{
  "my start time field": "2020-01-23T18:32:21.768Z",
  "my end time field": "2020-01-23T20:32:21.768Z"
}

I've reviewed: Using the range query with date fields. but I'm not sure how to only look at times. Also, I want to see if a time is between two fields, not if a field is between two times.

---

Essentially, the Elasticsearch equivalent of BETWEEN for SQL Server. Like this answer except I don't want to use the current time but a variable.

DECLARE @blah datetime2 = GETDATE()

SELECT  *
FROM Table1 T
WHERE CAST(@blah AS TIME) 
      BETWEEN cast(T.StartDate as TIME) AND cast(T.EndDate as TIME)

As per the suggestion from the OP and the link he provided which adheres to the laws of stackoverflow I'm providing the second solution in here:

Solution 2: Insert separate fields for hour minute as hh:mm

Note the format used which says hour_minute. You can find the list of formats available under the aforementioned link.

Basically you re-ingest the documents with a separate field that would have hour and minute values and execute range queries to get what you want.

Mapping:

PUT my_time_index
{
  "mappings": {
    "properties": {
      "start_time":{
        "type": "date",
        "format": "hour_minute"
      },
      "end_time":{
        "type": "date",
        "format": "hour_minute"
      }
    }
  }
}

Sample Document:

POST my_time_index/_doc/1
{
  "start_time": "18:32",
  "end_time": "20:32"
}

Query Request:

POST my_time_index/_search
{
  "query": {
    "bool": {
      "must": [
        {
          "range": {
            "start_time": {
              "gte": "18:00"
            }
          }
        },
        {
          "range": {
            "end_time": {
              "lte": "21:00"
            }
          }
        }
      ]
    }
  }
}

Let me know if this helps!