The relationships between men and women (boys and girls) can be confusing regardless of how careful you are with language. "I like your hat," could make some people clingy and desperate with a possessive infatuation. Currently, the expression, I have taken a shine to you seems to exist somewhere between, "I'm impressed," and "I think I love you."
take a shine to somebody (Cambridge Idioms Dictionary, 2nd ed. Copyright © Cambridge University Press 2006. Reproduced with permission.)
(informal)
to like someone immediately
I think Andrew has taken a bit of a shine to our new member of staff.
The etymology of shine:
1520s, "brightness," from shine (v.).
Meaning "polish given to a pair of boots" is from 1871.
Derogatory meaning "black person" is from 1908 (perhaps from
glossiness of skin or, on another guess, from frequent employment as
shoeshines).
Phrase to take a shine to "fancy" is American English slang from
1839, perhaps from shine up to "attempt to please as a suitor."
Shiner is from late 14c. as "something that shines;" sense of "black
eye" first recorded 1904.
Particularly in it's early usage the expression implied a romantic interest.
High life in New York, by Jonathan Slick, 1844:
If she wanted to take a shine to a Yankee, why couldn't she a found a
feller worth a looking at ? But sometimes it does seem as if these
gals couldn't tell bran when the bag's open — the brightest on 'em.
Dictionary of Americanism. - New-York, Bartlett 1848:
SHINE. To take a shine to a person, is to take a fancy to him or
her.
SHINE. To cut or make a shine, is to make a great display.
*All the boys and gals were going to camp-meetin'; so, to make a shine
with Sally, I took her a new parasol.*
The Knickerbocker, 1864:
'it 's rare to see a feller take a shine to a woman old enough to be his granmarm, but...
There were also times it was used without romantic implications, as in a 1900 edition of The American Magazine:
That's what makes it so ticklish dealin' with Indians; you can't tell
what they're thinkin', by their faces, any more 'n you can a clock.
But when they take a shine to a feller, they don't ask no questions.
A Dictionary of Slang, Jargon & Cant, 1890:
to take a shine, to be partial to a person or thing, to take a fancy
In 1898, the expression was used with the implications of "first impression", in The Deserter, and Other Stories:
... That's what made me take a shine to you, right off.
and in The Outlook - Volume 60:
Later he explained the matter to the teacher. "I didn't take a shine
to you nohow this morning," he said ; " I thought you was one of these
here psalm-singing gospel fellows, and I ain't got no use for that
kind. But when I seen you setting up there and a-eating pie with a
fork, I changed my mind. I knowed right away you was a gambler."
More recently the same range of meanings prevails. A Bride for Noah, 2013:
Uncle Miles, who had remained quiet until now, stepped forward. “It
seems some of our Indian friends have taken a shine to the ladies and
have taken steps to proclaim their feelings.”
Wild Animals and Wedding Outfits, 2013:
The Captain seems to have taken a shine to Bill's repertoire and keeps
exhorting him, 'Mr William, Mr William, give us a song!'
The Oxford Thesaurus of English, 2009, seems to have landed on the romantic implications, including it among various substitutes for fancy:
2 she'd fancied him for ages: be attracted to, find attractive, be
captivated by, be infatuated with, be taken with, desire; lust after,
burn for; informal have taken a shine to, have a crush on, have the
hots for, be wild/mad/crazy about ...
Realizing the historically strong implications of the phrase, the strong potential of misunderstanding between men and women, and your desire to prevent a possessive infatuation, it seems wise to avoid this expression.
Actually "sue me" means exactly what your dictionary says. It's kind of "fighting words" that imply the speaker does not apologize for his actions, and the only option the other guy has is to take him to court.
Which is silly, of course, because you can't sue someone for cutting into a line (or, as the British say, a queue). So in your example the offended person takes the next more extreme available option, which is to start a fight.
"Sue me" is actually relatively polite. There are many less polite options:
Kiss my ass!
Go to hell!
Piss off!
And the list goes downhill from there.
Best Answer
Yes, it is equivalent, but just slightly different. To draw a bead on means to line up a shot, as in hunting with a firearm, such that the shooter has the target in the gun's sight. Note that one only uses a firearm's sight when one is taking one's time, lying in wait, making sure one can do the job with a single shot.
To have a good bead on thus means, figuratively, to have a good, clear shot lined up. It suggests the people so described see the target clearly and have command of the situation. All that remains for them to do is pull the trigger.