There's some discussion in this thread; it appears that a USB Zip drive will "just work" with OS 10.12 (see post #7). It may be possible to install 10.12 to an external hard drive, boot from it, and then access the Zip disks from there.
Some months' back, I found a USB ZIP100 drive in the recycle bin at the recycle center, and brought it home. It looked like it was brand new.
I plugged it into my Mini before writing this, and inserted a ZIP100 disk (I've had around for MANY years).
The disk spun up and the icon mounted on the desktop.
So... we can be sure that the USB ZIP100 drive -DOES WORK- on a Mac running Mojave. It's sitting there running right now as I type this.
Do you have the ZIP drive connected?
If so, are any lights on (on the drive, WITHOUT a disk inserted into it)?
What happens when you insert a ZIP disk?
Does it spin up? (even if it doesn't mount on the desktop)
Answer these questions -- ALL of them.
Then we can go forward...