I'd previously forgotten about a machine I had still sitting in the Camry - a PC general with a missing case lid. I finally got around to testing it. Internally I found a 386DX-40 with VLBus. The motherboard is an OPTI-495 - traditionally a 486 VLB board, but this one has the 386 CPU soldered in, 386 BIOS, and an 80387 socket.
I spent much time fiddling about with 30 pin SIMMs - which can be quite frustrating trying to find four matching and working ones, while potentially having connection issues on a motherboard you're not even sure works. Eventually I did find two sets of working SIMMs, that after gentle encouragement are connecting reliably. I removed the very leaky CMOS battery and moved it in to a new case. I now have a working 386DX-40 with 8Mb RAM (8x1Mb 70ns 30pin SIMMs), VLB graphics, SB16, and a 170Mb Conner hard drive

One complication I did have but worked out fairly quick - was the Multi IO controller it came with had become a jumper donor at some point - eventually I found the right jumper and position to re-enable the floppy controller using good old fashioned guess-n-check. FDC is backwards - straight through = DS0, twisted = DS1 (with drives set to DS1). Was something I'd heard of but actually never had before (on a card anyway).
To finish I need to install the floppy drives properly, solder up an external battery, screw everything down and do a software install.