So, I got the board, it's a very decent performer (not the best, but definitely not the worst). It's also very stable, have been playing with it for the past week and have had no issues. Unfortunately, there isn't much that can be fine tuned further in order to increase performance... There are memory wait states that can be decreased in the BIOS advanced options, however any decrease results in a failed boot / graphical glitches (even with 60ns 30 PIN FPM memory). I'm guessing this is caused by the 40 MHz clock speed.
It still had the original battery which, amazingly, was able to hold a charge just fine. It looks like it was just starting to leak, though, so the timing was perfect. There was almost no corrosion (except just a tiny bit on one of the battery solder pads).
I removed the battery, got rid of the corrosion with a tissue soaked in white vinegar, cleaned the solder pads with a wick, reapplied fresh solder and finally cleaned the battery area with IPA.
It's unclear what board this is (although, it might be a BIOSTAR, because it looks very similar to the one in this thread). Mine has a soldered AMD 386 DX-40 (and it also supports an external 386 / 486DLC CPU).
J3 seems to be a connector for the external battery, but haven't tested it yet (the board works just fine without a battery).
All in all, the Macronix chipset looks like a solid chipset and those 8 KB of cache don't seem to cause any major bottlenecks. Some pics:
1 x PLCC-68 / 2 x PGA132 / 5 x Skt 3 / 9 x Skt 7 / 12 x SS7 / 1 x Skt 8 / 14 x Slot 1 / 5 x Slot A
5 x Skt 370 / 8 x Skt A / 2 x Skt 478 / 2 x Skt 754 / 3 x Skt 939 / 7 x LGA775 / 1 x LGA1155
Current PC: Ryzen 7 5800X3D
Backup PC: Core i7 7700k