Solving a Cipher: Celestial coordinates and precession

You guys were really helpful last time I came to you. Let's hope you can do it again. I have a sort of weird question, in a weird context. It's pretty complex, which is why I'm asking for help from experts. Let me explain. (Better grab a beverage, this will take awhile.)
I am not even an amateur astronomer. Bear with me.
I'm trying to solve a cipher (one of many) in a novel. I believe the key to this cipher is mapping constellations to the Earth's surface. Align 0 degrees GMT on the equator with the Vernal Equinox, and then translate hours and minutes of the celestial coordinates to terrestrial coordinates. Any given star or constellation's celestial coordinates will then map directly to a point on the Earth.
I understand that the Earth moves, so the coordinates must be fixed and constant. Vernal equinox = 0N, 0W on the equator.
SPOILER ALERT: I think precession might come into play.
Sagittarius is at 19h RA, -25 Dec. precisely.
That maps to 75W, 25S on the Earth. It's just off the coast of Chile. There's a town named Caldera a little southeast of there. The name Caldeira is very important in this novel. So is the Archer (Sagittarius). So is the number 19. As in 19h Right Ascension. Drifting constellations was the theme of one chapter. Constellations moving and falling apart.
Hold onto that thought, if possible. I know this is insanely complicated. I trust you can follow me, if I don't mess this up.
This novel comes with a sort of decoding wheel. It's a disc with N-S coordinates, on a disc with E-W coordinates. You turn the discs so the coordinates you want align, and then look in a little window to get letters to solve a cipher. What's weird about it is that there's an extra seven degrees for each cardinal direction. West and East start at 0 (GMT), but each goes to 187 degrees, for an extra 14 degrees total. N and S start at 0 (equator), but each goes to 97 degrees, beyond the poles. No one has ever explained this.
I think I can.
Those extra 7 degrees indicate precession. The celestial coordinates move with Earth's precession.
I think there was a point in time when Sagittarius was directly over Caldera, Chile.
So here's my question: how can I calculate the date(s) that Sagittarius was directly over Caldera? Is there an online thingy I could use? There are other constellations in the novel, and I want to look at where they were, too.
Sorry to be so long-winded. I feel that if you know what I'm doing you'll be better able to help me. Also, maybe you'll have insight I'd never see.
"S." by Doug Dorst and JJ Abrams.

It's presented as a 1949 novel by fictional author VM Straka, titled "The Ship of Theseus." In the margins are hand-written notes by a grad student, Eric, and an undergrad, Jen, who are both trying to figure out who Straka was, and whether the cabal known as "The S" really exist. They've inserted post cards and newspaper clippings and other documents between the pages. Their story and the story of Straka and his translator, Caldeira, often reflect each other. Caldeira left clues in the footnotes for Straka to find so he could solve ciphers so they could re-connect. Also to warn him that his enemies were still after him. See, Straka faked his own death and...

It's really complicated. I've been wrestling with it off and on for five years now. There's a Web community of people collaborating on it. Only a few die-hard stragglers are still plugging away. I've made some important discoveries, and I think this one might be the most important of all.

If you like rabbit holes, this is for you.

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