I'm planning on getting a Zip drive for my Classic II one of these days.

Anyway, here's some info on using Zip Drives on Old Macs:

Mac Plus and Zip Drives Revisited (I'd recommend reading this one first, it has some useful info on driver issues.)

Using A Zip Drive On A Mac Plus

Mac Plus and using a zip drive as a hard drive (Apparently, some of the Plus ROMs possibly had SCSI issues.)

Click-Death Fix Guide (... Just in case.)

Hopefully there is something useful among all that data.

Edit: Oh Hmm, well. Coius could very well be right. Considering that your 512k has third party SCSI.