There are a 101 things that can go wrong. But some pointers
1) Each lamp is daisy chained to next so work on one lamp can stop the next lamp working.
2) Using any neon tester will not test the neutral only testers with two connections can test neutral is also sound.
3) A fuse can allow enough current to flow to light a neon even when it has blown. Again continuity tester with two wires or swap fuse to test.
4) Sometimes MCB's can trip without moving the switch like reset button/switch always worth switching off and back on. You can normally feel a faulty MCB switching off and back on a MCB to a known good circuit should show you what it should feel like.
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