.. How do I learn Charles's password?

This is another case in which Joey will eavesdrop on the brothers and hear them spill the beans. But Rosa needs to shake them up first.

After you've learned all you can about the two mysterious deaths --

How do I find out more about Frank's death?

What do I do after Claude's death?

-- go to the lighthouse and talk to the man who's now there.

How do I get the man at the lighthouse to talk to me?

When you've researched everything the man at the lighthouse told you and found the connection to Meltzer, come back and talk to them about it.

The brothers are understandably upset and ask Rosa to leave. Do so, but have Joey stay and listen for a bit.

If you've done everything you need to do, you'll hear Paul call Charles "Scooter." That's the password you're after. (But as with Paul's password, it won't work until you've heard Paul say it in the game.)