The "slot" that the pin rests in should have had a metal bar across it, with a screw on either end. See whether you can't see evidence of that.
In any case, you would have to secure a suitable pivot pin. The one thing I'm not sure of is whether the pin should go in a bushing or epoxied into the blade.
Other than that, the details are similar to a rudder. However, while I built a rudder successfully from plywood (it's still hanging in there), I would not recommend that approach for a centerboard.
For that you start with some suitably rot-resistant and suitably strong would that you rip into slats. You then assemble them into a board by stacking them so the cross-grain alternates (and the long direction of the slats aligns with the centerboard). There's this special waterproof wood glue (resorcinol-formaldehyde) that would be ideal for something that's immersed. Better than epoxy or Titebond. (Epoxy is generally a good glue, but it can separate from waterlogged wood).
Once you have a board, you need to cut the correct outline - details and drawings to be found on the DSA main website
https://daysailer.org as part of the bylaws. (Above the bottom of the hull it's squared off with rounded corners if memory serves). You then cut the tip off at an angle and glue it back on. That glue line will impede any water wicking up the board should the tip get damaged.
Then you need to locate a suitable foil shape, something like the NACA009 profile. You need to find a way to take the correct excess wood off to be left with the shape you want. (The part above the bottom the hull should not be shaped and left flat).
Finally, you drill the holes for the pivot and attaching the cables.
Now you can seal the whole board in epoxy and also give it a very light sheath of fiberglass. After that you can fair and paint it.
One thing that some people do is to route a shallow channel running the length of either side at the widest part of the board and embed a couple of layers of biaxial or woven rovings, for extra strength in a crucial direction).
In a way, from a woodworking perspective it's just a specially shaped cutting board.
There are some old DaySailer Quarterly magazine articles on how to build one, but you may have to spring for DSA membership to access the archives. (A steal at $35.00 and also funds the hosting of this forum - if you do, be aware that the two sites use unrelated and therefore potentially different username/password credentials).