Now that I have seen the internal view (obviously Techie based because the letters omit I and O to avoid confusion with 0 and 1, and it does allow the designer to instruct the person with the soldering iron with unambiguous instructions like "join G5 to G6") it does look like the board layout and the machine it went into were designed as a combination. The fact that there are unused pins does suggest that the target machine could do more than one thing depending on the connections on the board inserted. There also will need data connections feeding what was read from the card or paper tape either electrically (a wire making contact with the drum feeding the card or tape, or else photo-electrically) into the machine. There will be one reader per column or row depending on how the source information is presented, so there will have to be a timing pulse that can be counted to know where the hole is in relation to the medium on which it is found.
That suggests the data connections are the bulk of the connections (perhaps the vertical ones) and the functional connections are in the areas where the pins are more sparse (and there are a few horizontal connections). If that is the case, then this board has the potential for
48 readable positions of which 32 are wired for use. The Census card I found had 48 columns, though I have no way of telling whether that is an indication of function of this board or just a coincidence.Some modern electronic equipment has jumper switches to tell the works whether it is in set-up mode or operational mode (I have got a thermostat that has a wire free connection to the operating box, and that has a jumper for telling the remote box that it should obey this thermostat, after which the jumper is unset and the remote box does what that thermostat tells it). I wonder if the soldered pins without a wire indicates a jumper position wired for testing and removed for live running? The earlier home computers had PATA connections for magnetic discs or optical discs. These could handle a daisy-chain of two devices, and there was a jumper on each device to identify it as either master or slave (I think that was to indicate that the master was the boot device) so that the processor knew which of the two devices was providing input and any given time.
A fascinating puzzle, Another John, and I hope my musings lead you to others with more historical knowledge that I have. If you do find the answer, can you report back to this group?