verb-ing modifier trouble

It modifies the researchers. Why?

It's very simple. We see that the verb-ing modifier clause is "Searching for signs of life on Mars". The verb is "searching". Now ask yourself: who or what is doing the searching? Upon asking this question, we see that it is the researchers who are searching.

There's really nothing to study for over here for these types of questions. Just run through the same procedure every time: ask who or what is doing the verb. You'll always get your answer if you do that.

Various grammars interpret this in different ways. Here a but a couple of them . . .

(Warning: grammar terms vary!)

Adverb modifying verb:

Searching for signs of life on Mars is a reduced adverb clause. You can think of it as being reduced from a full clause like this:

Because they are searching for signs of life on Mars, researchers have sent many probe rovers to the planet.
Searching for signs of life on Mars, researchers have sent many probe rovers to the planet.

The adverb clause functions as an adverb, so it's not (under normal circumstances) going to modify a noun. It answers the question of why? for the verb (or the whole independent clause, really): Why have they sent rovers? Because they were searching for signs of life.

Adjective modifying noun:

Searching for signs of life on Mars is a participle phrase functioning as an adjective. It may help you to think of it as being reduced from a full relative (adjective) clause like this:

Researchers who are searching for signs of life on Mars have sent many probe rovers to the planet.
Researchers searching for signs of life on Mars have sent many probe rovers to the planet.
Searching for signs of life on Mars, researchers have sent many probe rovers to the planet.

In the end, you'll want to understand it as your own grammar source dictates, but at least this might help you with an approach.