"Sought" vs. "searched"

This is very squishy, actually. In some cases you could interchange them and no problem with it. But in others you couldn't. In your example, they are equivalent.

"Seek"/"Sought" can be quite passive or much less active than "Search/Searched". "Seek" can be quite theoretical, which "search" is not.

• "I seek for the greater good of all mankind." I can sit in my easy chair and do this with my eyes closed, snoring softly.
• "I search for the greater good of all mankind." This implies I am out of my chair and actively looking for it, as if it were some discreet object.

This isn't ironclad in all cases, however. You could use "seek" like you would use "search", but possibly not the other way around. In the children's game of "Hide and Seek", the seeker is definitely actively looking. Unless being "It" was a ploy to have a little peace and quiet away from the "Hider".