Pb with formating column

Hello, 🙂
I would like to format a column in a list.
This column displays the name of a person in our AD along with their email address. I found the JSON code in this community.
When the column doesn't correspond to an AD user, I would like to display text located in another column.
To do this, I included a condition in the code. But it doesn't work. The field remains empty when the person is not associated with the column.

The portion of code that is probably problematic : 

"txtContent": "=if([$person.title] == '', [$FullName], [$person.title])"

$FullName is the name of an other column :

    {
        "CellPhone": "XX XX XX XX XX",
        "ContentType": "Contact",
        "ContentTypeId": "0x01060062E91085FE5F6C468F33BBF1D871B1F7",
        "FileRef": "/sites/dsnb/it/Lists/Phones/1_.000",
        "FirstName": "",
        "FolderChildCount": "0",
        "FSObjType": "0",
        "FullName": "SERVICE 01",
        "ID": "1",
        "ItemChildCount": "0",
        "PermMask": "0x7ffeffffffffffff",
        "SMTotalSize": "236",
        "WorkPhone": ""
    },
    {
        "CellPhone": "YY YY YY YY YY",
        "ContentType": "Contact",
        "ContentTypeId": "0x01060062E91085FE5F6C468F33BBF1D871B1F7",
        "FileRef": "/sites/dsnb/it/Lists/Phones/2_.000",
        "FirstName": "Toto",
        "FolderChildCount": "0",
        "FSObjType": "0",
        "FullName": "SERVICE 02",
        "ID": "2",
        "ItemChildCount": "0",
        "PermMask": "0x7ffeffffffffffff",
        "SMTotalSize": "296",
        "WorkPhone": "AA AA AA AA AA"
    }

Could you please help me with this?
Thank you in advance.

Ci-dessous le code JSON :

{
    "$schema": "https://developer.microsoft.com/json-schemas/sp/v2/column-formatting.schema.json",
    "children": [
        {
            "elmType": "div",
            "style": {
                "background-color": "=if(length(@currentField) == 0, '#ddd', '#aaa'",
                "border-radius": "1.5em",
                "color": "white",
                "height": "1.5em",
                "min-width": "1.5em",
                "position": "absolute",
                "right": "1em",
                "text-align": "center",
                "top": "0"
            },
            "txtContent": "=length(@currentField)"
        },
        {
            "children": [
                {
                    "children": [
                        {
                            "attributes": {
                                "href": "='mailto:' + [$person.email]"
                            },
                            "children": [
                                {
                                    "elmType": "div",
                                    "style": {
                                        "font-size": "1.2em"
                                    },
                                    "txtContent": "=if([$person.title] == '', [$Fullname], [$person.title])"
                                },
                                {
                                    "elmType": "div",
                                    "style": {
                                        "color": "gray"
                                    },
                                    "txtContent": "[$person.email]"
                                }
                            ],
                            "elmType": "a",
                            "style": {
                                "margin-left": "0.5em"
                            }
                        }
                    ],
                    "elmType": "div",
                    "style": {
                        "display": "flex",
                        "flex-direction": "row",
                        "justify-content": "center"
                    }
                }
            ],
            "elmType": "div",
            "forEach": "person in @currentField",
            "style": {
                "justify-content": "center",
                "margin-top": "=if(loopIndex('person') == 0, '0', '1em')"
            }
        }
    ],
    "elmType": "div",
    "style": {
        "align-items": "start",
        "flex-direction": "column",
        "min-height": "1.5em"
    }
}