Just wondering if you are even using the Volt-Ohm meter correctly. If you are using the setting that "beeps" the VOM when the leads are touched together that is for measuring resistance.
You want to use the DC volt setting. This should read 12 volts when directly connected to battery.
From your set up the bare wires are not causing the problem. IN fact they should be a benefit as touching them together SHOULD cause the brake lights to come on. IF touching the bare wires together does not cause the 3rd high mount brake light to come on THEN there are other things wrong here.
You need to go back an perform the tests to prevent a wild goose chase. Must of the previous advice was given with the understand there is +12 volts present at one of the leads going to the BOO switch.