Hi, first ignore low voltage readings as If using a digital multi meter they simply indicate an open circuit, & should NEVER be used for fault finding on mains circuits nor should neon test screwdrivers!! Both can give totally misleading indications.
the 3 common reds are only looping in & out to next fitting plus taking live to 1st switch, so should be in terms marked 'loop' and don't connect to flex.
the 3 blacks correctly identified as Nuetrals should go into the 2 terms next to the blue of flex.
the remaining 2 switch lines (red sleeved blacks) should go in the 1 term next to the brown of flex.
you have checked for 240V common lives to Neutrals ok.
You should now check sw.lines (red sleeved blacks) to Neutral (blacks) for 240-0-240-0 with switch being operated by someone.
Most likely reason for non operation is a wire in the wrong term of rose.
I have tried to read what you say you have and match it to standard systems but it does not seem to fit in. Too many black wires. I have seen twin and earth with two red wires but never two black so one would expect equal or more reds than black.
As to the 6 volt and 5.5 volt thatâ€™s from capacitance between the two wires running very close and can be ignored. It looks as though you have lost supply to the switch. About the only thing I can do is explain three way switching which may help you.
It you look at wikipedia it gives the typical school boy method but although this works it would require a joints inside each switch so the line and return are connected to the L1 and L2 of the first switch not the common, Then a three core cable is run to the other two way switch and all cores connected like for like so L1 on switch 1 connects to L1 on switch 2 etc. This means switch one will have two wires in both L1 and L2. When a third switch is used the is different from other two and is called an intermediate switch. This takes the L1 and L2 wires only from both other switches and the common wire is normally joined with a small terminal block inside the switch backing box. This method of wiring means at the lamp there is no difference to how many switches are used one cable will have feed to and return from the switch or switches. One will go to permanent line connection and the other to the lamp. (Note because neutral is considered as live we use line to mean phase wire on a single phase supply) so starting at the two terminal block on the rose we have 1 Switch to lamp. 2 Switch from switch. 3,4,5 Line from previous lamp, Line to next lamp, Line to switch (Not necessary in that order) 6,7 Neutral form previous lamp, neutral to next lamp (Not necessary in that order) 8 neutral to lamp. There can be variations where either two lamps feed off same switch or if there are two â€œnextâ€
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