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Google Sheets move cursor onEdit trigger based on cell content

I am trying to write a Google Sheets Apps Script function that checks the content of the current active cell, matches it to the content of another cell, then moves the cursor according to the result of that check.

For a spreadsheet as this example one:
https://docs.google.com/spreadsheets/d/1kpuVT1ZkK0iOSy_nGNPxvXPTFJrX-0JgNmEev6U--5c/edit#gid=0

I would like the user to go to D2, enter a value followed by Tab, then while the active cell is in E2, the function will check if the value in D2 is the same in B2. If it is, stays in E2.
Then we enter the value in E2 followed by Tab, the function checks if it's the same as C2, if it is, then moves from F2 down and left twice to D3. So if all the values are entered correctly, the cursor zig-zags between the cells in D, E and F as shown below:

The closest I could find is the answer to the one below, but it involves clicking on a method in the menu each time:

Move sheet rows on based on their value in a given column

I imagine the function could be triggered at the beginning of editing the document, then it keeps moving the cursor until the document is completed, at which point the function can be stopped.

Any ideas?

EDIT: what I've tried so far:

I have managed to change the position to a hard-coded position 'D3' and to create a function that moves one down with these functions:

function onOpen() {
var m = SpreadsheetApp.getUi().createMenu('Move');
m.addItem('Move to D3', 'move').addToUi();
m.addItem('Move to one below', 'move2').addToUi();
m.addItem('Move down left', 'move_down_left').addToUi();
}

function move() {
var ss = SpreadsheetApp.getActiveSpreadsheet();
var s = ss.getActiveSheet();
var range = s.getRange('D3');
s.setActiveRange(range);
}

function move2() {
var ss = SpreadsheetApp.getActiveSpreadsheet();
var s = ss.getActiveSheet();
var r = s.getActiveRange();
var c = r.getCell(1,1);
var target = s.getRange(c.getRow() + 1, c.getColumn());
s.setActiveRange(target);
}

function move_down_left() {
var ss = SpreadsheetApp.getActiveSpreadsheet();
var s = ss.getActiveSheet();
var r = s.getActiveRange();
var c0 = r.getCell(1,1);
var r1 = s.getRange(c0.getRow(), c0.getColumn() - 1);
var c1 = r1.getCell(1,1);
var r2 = s.getRange(c1.getRow(), c1.getColumn() - 2);
var c2 = r2.getCell(1,1);
if (c1.getValue() == c2.getValue()) {
var target = s.getRange(c1.getRow() + 1, c1.getColumn() - 1);
s.setActiveRange(target);
}
}


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onEdit

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