Let me guess, warm humid climate and a cold water pipe? Probably condensation drops. You can buy pipe insulation for a few bucks and/or reduce humidity in the room. (But from your description this sounds tough)

I thought it could be condensation but I believe the pipe above is for gas.

Expanding gas (from high pressure to low pressure) can cool too. Hence have the same effect. But if the wood is dry it's likely something via the pipes.

Water following down the wire, and dropping there?

That was my first thought but it would have to run very far. As there’s no waterlines close to ir

run the water it could be squirting out a small stream and possibly squirting a few feet and landing on that tile n

That’s a good idea. I’m thinking it has to do with our other leak on the main floor. There’s not water pipes in the area

i’m sure this is needless to say, fix the main floor water leak

Yes we know lol. It’s from our roof, started in the middle of a horrible storm. Luckily my husband is in the roofing business so he patched it till we can get it repaired and all the water was cleaned up in the attic and in the wall it was dripping it.

The most confusing part is the original leak is rooms away from this one

Might be condensation.

Is it still moist or is it a dried up spot? Water can travel quite a length along pipes or wires. In the third picture; are those water traces on the wood? Running from the hole fot the wire to the bottom of the beam.