You have 4 connections it would seem likely the casing is earthed it should be, I am considering that as a connection, I would normally use a meter starting with one lead on casing measure other three, then select one of three, measure to other two, and then across other two.
This should show if there is any supply there. Assuming you find a supply next is to find out what switches off the supply, only then can you use the supply.
Often physically tracing the cable is the best start, you look at where the conduit goes, and look for switches or fuses which would likely feed it, it is far easier working out what feeds what while it is still working, and first job in any new house should be to inspect the electrics and if nothing else ensure all fuses or MCB's are marked as to what they do. I have looked up into the ceiling when my bath leaked and thought what do those wires feed, and I am the only person to have lived in the house, you need to write it all down and put with or close to the fuse box/consumer unit.
You may find out what switches the conduit box you show while doing that, I don't like the neon screwdriver but even one of those is a start, as it stands it could be anything, you need to hunt as even if dead it may only need a switch flicking or a fuse replacing.
One thing to remember, if I was in a house and the outside light failed just before selling I would simply remove the fuse, if the wiring was damaged, I would remove the fuse, also may drop the tails in the supply. So finding out where it is supplied from and simply fitting a new fuse may work OK, but it may not be safe, as you have no idea why the fuse was removed. It is harder to reuse old wiring than put in new, as you need to inspect and test before energising to ensure there is no branch as you could be also energising bare wires you have yet to find.
So use your eyes and try and trace where coming from and going to before energising. In theory you should get an electrical installation condition report it was called a periodic inspection report when a new occupant moves into a home. This report should highlight any problems, and expose any DIY work done by previous occupants which may be dangerous, it can't find every fault, but it means your starting on a level playing field, even without anyone doing something wrong, you can get a combination of events over the years which change things.
I know in my dad's house as a child I touched a live wire to earth and it ruptured the fuse, so I know there was a good earth, however when the new consumer unit was fitted, the only earth that could be found was the one for the old post office party line telephone. Something had changed over the years, likely original earth was through water pipes which have been removed, but fact was there was no longer any earth. Maybe a man had changed the meter and left it off? We simply do not know. Which is why we also have an EICR done every 10 years (3 years in Scotland I think?) before getting into DIY it may be best to get an EICR done!
