This would be better done in daylight.
1st, the tester you are using is a proximity tester, and you'll need a VOM (volt, ohm, meter) and it doesn't need to be expensive.
2nd, if you have fuses or breaker you'll need to shut the one off that controls the light switches you want to work on.
3rd, disassemble the 2 switches that control the stairway light. if you can remember where the wires go, or you can label them.
Turn the power back on and find which conductor/s have power, It should only be one.
With the power back off, twist the other 2 conductor form one of the switches together, and with the VOM on an ohms scale attach the leades to the 2 conductors of the other switch, and if there is continuity the meter will deflect to "0".