What sort of crazy ignition gimmick is this?

First, the inner and outer coil terminal connections on those terminal pieces are insulated from each other. Those may be "chunks" of circuit board. What they have done is to provide an easy place to separate the original wiring, and to route the CD system to the coil

So the part of the terminal board that bolts to the coil is the fired high voltage pulse output of the CD. As I explained earlier, this works very similar to a photoflash

The original car coil wires fasten to the outside terminals of the board, and are routed back to the CD unit. IF you examine, you'll see that the cabling going from the board terminal pieces to the CD is 4 wires

Now, what you just posted is a "thing" I had not counted on.

Originally, these were designed to be triggered by points as I said. What they are doing, is the same 12V power on the original coil+ terminal is routed to the CD. The BLACK (I think) that originally went from the OEM breakerless box MIMICKS the points action, that is, the breakerless distributor triggers the OEM box and switches the coil on/off just like it had points. So that black? wire coming from the OEM breakerless is triggering the CD

That box, now leaking, may or may not have a problem.

I would connect the original OEM coil wiring back to the coil and see if it will make spark. As I said earlier, I WOULD NOT attempt to use that CD box for a number of reasons

Here is a poor quality crop from that link I provided earlier:

https://selectric.org/delta/index.html
You can sort of see the separation of the coil terminals.

What they are not grapically depicting, here, is that the OEM wiring connects to the OUTER terminals. The power from the "run" wire connects to the far left, and the lead from either points, or (in your case) the swithing wire from the OEM breakerless connects to far right. THESE ARE FOUR INSULATED terminals.

instructions02.jpg

The Great Big Red Print from Zed L land has not been here, I see.