the primary key is SO important that it's better to NOT show it.
BTW: only for your eyes, you can simply put that field on a layout based on the Contact Table.
Should I always be able to see it as a field in the table itself in databases? If so, any ideas which one it is for the contacts database that filmaker makes available?
Unlike other RDBMs, Filemaker does not have a "native" primary key. There is a unique RecordID, which you can see using the Get (RecordID) function - but you should NOT use this as your primary key for relationships. You need to create your own primary key, which is best done by having a field with auto-entered serial number in every table.
I am not familiar with the template you mention, but surely you can see which fields are being used as matchfields from the relationships graph?