Google-sheets – Limiting range in OnEdit timestamp script

I've modified the code from my answer to fit your description. In the example below, columns 2-5 (that is, B-E) of sheet named 'Sheet1' are monitored for changes. In case of change, a timestamp is inserted in the last row of that column.

To customize: change the sheetname and column bounds on line 4 of the script. If a non-contiguous range of columns is to be watched (e.g., columns 2,4,7,8), replace the conditions column >= 2 && column <= 5 with, for example, [2, 4, 7, 8].indexOf(column) > -1

function onEdit(e) {
  var sheet = e.range.getSheet();
  var column = e.range.getColumn();
  if (sheet.getSheetName() == 'Sheet1' && column >= 2 && column <= 5) {
    var row = sheet.getMaxRows();
    sheet.getRange(row, column).setValue(new Date());
  }
}

The active range is not set at user level, it is set separately for each user session with a spreadsheet. That is, the same user can open the spreadsheet in two tabs of a browser and have two different cursors (active ranges) in each. (You'll see the other one shown in green, with your own name on it).

When your script is called manually, it affects the user session from which it is called. When it is invoked by a trigger, it affects the user session created for the event of form submission. That session is separate (and short-lived), so setActiveRange does not do anything visible in practice.

To demonstrate this, one can use the following minimal example, triggered by form submission. (So we don't have to think about nested while loops and whatnot.)

function test() {
  var sheet = SpreadsheetApp.getActiveSheet();
  var range = sheet.getRange("B2");
  sheet.setActiveRange(range);
}