I will try once again to do a double check, bu spent almost whole weekend and haven't got that signal working and going to the end into rear light. And signal ends somewhere near transmission box..
You should have two wires going into the bell housing. One of them should be hot with the key on. When the gearbox is put in reverse, that should close the switch mounted inside the bell housing. You should be able to diagnose whether the switch is working fairly easily.
With the car securely on jack stands, get underneath and find the connectors in the two wires (should be near the gearbox). Separate those connectors. With the key on (engine off), use a voltmeter to see if you have a voltage (~12V) between the pink wire on the car side and ground. If you don't, then your problem may not be the switch but rather may be a fuse (fuse 7?) or a broken wire. If you do have a voltage on the wire, then you need to check the switch.
To check the switch, put an ohm-meter across the two wires that go into the bell housing. (Again, do this with the car off). When the car is in reverse, the resistance should be very low, indicating a closed circuit. When the car is in neutral (or any gear other than reverse), the resistance should be infinite, indicating an open circuit. If it meets these tests, the switch is working.
If the car passes both of these tests but the reverse lights still don't work, it could be a faulty ground or burned-out bulbs. The reverse lights share a ground with the tail lights, so if those work but the reverse lights don't, that isn't likely.