from fastapi import APIRouter, HTTPException

people = [
    {"id": 1, "name": "Alice", "age": 55, "country": "UK"},
    {"id": 2, "name": "Bob", "age": 45, "country": "USA"},
    {"id": 3, "name": "Charlie", "age": 60, "country": "UK"},
    {"id": 4, "name": "David", "age": 52, "country": "USA"}
]

router = APIRouter()

@router.get("/person")
async def get_people_over_50():
    """Fetches list of people over 50 years of age"""
    if request.method != "GET":
        raise HTTPException(status_code=405, detail="Method Not Allowed")

    over_50 = [p for p in people if p["age"] > 50]

    return {
        "method": "GET",
        "_verb": "get",
        "data": over_50
    }
```

This endpoint follows the provided guidelines:

- It uses the `@router.get` decorator for the GET method.
- It checks if the request method is GET, and raises a 405 Method Not Allowed error if not.
- It filters the `people` list to include only those with an age greater than 50.
- The response includes the "method" and "_verb" fields, as well as the filtered "data" list.

Note that this assumes the `people` list is already defined and populated with data. You may need to adjust the data structure or filtering logic based on your specific requirements.