I would like to know if the term 'in the gun' is commonly understood
in the way I understand it - meaning 'being hunted down' or 'under
close and critical scrutiny'. I need this for a song I'm writing.
(the Google search engine is no use to me because it eliminates the
'in the' part of the saying ('in' and 'the' are too common) - and
comes up with lots of responses about the gun industry.

Hi, 

Your commenter below is more or less correct. Under the Gun is the
commonly held phrase for the meaning you have described. "In the Gun"
usually is a descriptive phrase for "ready to be fired" or used as
"Faith In the Gun" or meanings of that nature.

When searching using Google (or any other major search engine), for
phrases such as these, you will get more mileage out of using advanced
type searches. For example :

+"in the gun" (using the + sign and quotes around the text)

or 

+"in the gun"  +lyric (adding +lyric narrows the search to pages where
the quoted text is in, or has to do with lyrics).

Something to keep in mind with commonly used phrases, is they were not
common before someone stuck them in a song and created the menaing
behind it by the rest of the song. Depending on the rest of your
lyrics, 'in the gun' may not be popular, but may still be meaningful.

://www.google.com/search?sourceid=mozclient&ie=utf-8&oe=utf-8&q=%2B%22in+the+gun%22+%2Blyric
 that is a link which searches for your song lyrics 

://www.google.com/search?sourceid=mozclient&ie=utf-8&oe=utf-8&q=%2B%22under+the+gun%22+%2Blyric
this one searches for "Under the Gun"

thanks, 

webadept-ga

Very helpful. More than just a 'here's your answer' take it or leave it.
The answer was nicely supplemented by the Comment. I will modify my
lyrics to 'under the gun' from 'in the gun' accordingly. I will be
singing the song to 1,000 people at a gala dinner in two weeks).

I will definitely use this service again (it was my first time)

I have never heard of "in the gun" as an idiomatic phrase with the
meaning you describe. However, "under the gun" has this meaning.

http://www.goenglish.com/0803.asp

Howdy david011295-ga, 

There is also "in the sights of a gun."

Google search on: "in the sights of a gun"
://www.google.com/search?q=%22in+the+sights+of+a+gun%22

Google search on: "in the sights of your gun"
://www.google.com/search?q=%22in+the+sights+of+your+gun%22

Just "in the sights" could work.

Google search on: "in the sights" lyrics
://www.google.com/search?q=%22in+the+sights%22+lyrics

From Bruce Springsteen's "Point Blank."

"You're walkin' in the sights, girl of point blank
and it's one false move and baby the lights go out ..."

This might make a nice lyric such as "I knew it was over when
I was caught in the sights of your love" or the like.

There is "in your sights" as well.

Google search on: "in your sights"
://www.google.com/search?q=%22in+your+sights%22

Google search on: "in your sights" lyrics
://www.google.com/search?q=%22in+your+sights%22+lyrics

From Def Leppard's "Love Bites."

"If you've got love in your sights
Watch out, love bites ..."

Looking Forward, denco-ga - Google Answers Researcher

To pinkfreud-ga and to denco-pa - many thanks for the time you spent on this
query. You - together with the official 'answer provider' have fixed up my problem
 - so it's 'case closed'. I will use 'under the gun' instead of 'in the gun'.

Our pleasure, david011295-ga.

Good luck with your gala dinner performance!

Looking Forward, denco-ga - Google Answers Researcher

For future reference, you can use " " marks in google searches.