Here's what I have done. By the way, I'm using Windows 7.
First, I copy the files from the second disc (it has the installation on it) to a new folder, "7th".

Z:\>mount c "c:\7th"
Drive C is mounted as local directory c:\7th\

Then, I mount the disc itself.

Z:\>mount d "f:\" -t cdrom
MSCDEX installed.
Drive D is mounted as CDRom f:\

Z:\>d:

D:\>install

Then, the installation begins and I choose to copy the game files to the C drive: "C:\t7g", I choose SVGA as the video mode, and I choose Sound Blaster ASP/16 as the sound driver. The installer copies the files to "C:\t7g" and the installation is complete. DOSBox immediately says:

Type T7G and the ENTER key to play The 7th Guest.

C:\T7G>

So, I do.

C:\T7G>t7g

Then, the game starts and tells me to "Please Insert Disc One" so, I do. I hit ctrl-f4 to have DOSBox read this new disc and I click to continue as the game prompts me to do. The game goes to its Load or Start New screen. I hit "Start New" and a popup from DOSBox tells me "The wrong volume is in the drive. Please insert volume T7G_DISC2 into drive F:." with the clickable options cancel, try again, and continue. Hitting all three just makes a second duplicate popup so, I switch discs, hit ctrl-f4, and hit continue. The game begins and the opening video plays, but once the video ends, so does the game. DOSBox tells me:

Error: GJD file system error - aborting

C:\T7G>

I don't know what to do at this point so I enter t7g again.

C:\T7G>t7g

And the "please insert disc one" screen reappears. I do and everything fails just as it did before.
I'm so confused.

EDIT: I realized after hitting cancel twice on the DOSBox popup, the game would still continue and even go into the actual game just so long as I don't switch back to disc 2. The real problem is that once I quit DOSBox, I can't start the game without reinstalling everything. Which is a big pain but it also means losing any saved data, I think. I'm not even sure where DOSBox is sending this saved game data or how to access it. Or if it even still exists.