onEdit function in google sheets seems its not working at all

function update_supervisor_drop_down() {
  var ss = SpreadsheetApp.getActiveSpreadsheet();
  var sheet = ss.getSheetByName("Sheet6");
  var data = sheet.getRange("E1:F").getValues();
  var list = [];
  for (var i = 0; i < data.length; i++) {
    if (data[i][1] === "supervisor") {
      list.push(data[i][0]);
    }
  }
  var rule = SpreadsheetApp.newDataValidation().requireValueInList(list).build();
  sheet.getRange("B:B").setDataValidation(null);
  sheet.getRange("B1:B5").setDataValidation(rule);
}

function onEdit(e) {
  var ss = SpreadsheetApp.getActiveSpreadsheet();
  var sheet = ss.getSheetByName(e.source.getActiveSheet().getSheetName());
  var range = e.range;
  if (range === "E1:F") {
    update_supervisor_drop_down();
  }
}

Basicly I have 2 functions, the first one is working like a charm after I save and run the script.
My problem is in the second onEdit function that is supposed to execute the first function if range E1:F is edited, but its not working when I edit the specified range.
Any idea how to solve this issue ?
Thanks

I tried alot of code snippits one of which is this:

function onEdit(e){
  var range = e.range;
  var sheetName = e.source.getActiveSheet().getSheetName();
  if ( // E1:F on "Sheet6"
    sheetName == "Sheet6" &&
    range.rowStart >= 1 &&
    range.columnStart >= 5 &&
    range.columEnd <= 6
  ) {
    update_supervisor_drop_down()
  }
}

Based on your sample, I understand that you want to run the function update_supervisor_drop_down() when you edit columns E:F.

Try updating your onEdit(e) function to this:

function onEdit(e) {
  var ss = SpreadsheetApp.getActiveSpreadsheet();
  var sheet = ss.getSheetByName(e.source.getActiveSheet().getSheetName());
  var range = e.range.getColumn();
  if (range === 5 || range === 6) {
    update_supervisor_drop_down();
  }
}

I tested it and it worked. Let me know if you have questions.

Reference:

getColumn()