B16A1 and B16A2 are not JDM engines. You are confusing me. Both the first and second generation B16A's were marked "B16A."

If you have an OBD-1 first gen B16 it probably came from a '92 Integra XSi. It is a very unusual and uncommon swap.

I would personally backdate the engine to OBD-0, it will make life a lot easier vs. swapping/reworking the chassis wiring. For best results, you could find a guy with a 92-93 Integra who wants a B16A swap but has an OBD-0 engine and trade your OBD-1 for his OBD-0 unit.