Answer:

This is how it works in the B2T direction:  

1.  Insert a new Constituent record in CRM, which will cause a trigger to insert a record into a table called TA_NEWCONSTITUENT.
2.  When the sync runs, it will create new sync records for those Constituents, so that it can sync it over to TA.

Fix:

1.  Insert the ID for the CONSTITUENT record in CRM into the table TA_NEWCONSTITUENT.
2.  The sync will create a TA_CONSTITUENT record for it and then try to sync it.

From SDM:

-- Get ID from CONSTITUENT table using the LookupID:
 
SELECT ID FROM CONSTITUENT
WHERE LOOKUPID = '8-11882482';

-- Add new record in TA_NEWCONSTITUENT table using the ID from above query:
INSERT INTO DBO.TA_NEWCONSTITUENT (ID)
    VALUES ('94fc4ea3-2751-4d33-b884-fc2b3cd0cf3c');

In this case, after running the insert, the next sync will create the Name record (from the Constituent info) in TA as Name_ID 2 (since Name_ID 0 and 1 already existed), and the LookupID on the constituent should be TA616557002 (TA + Account_ID + 2-digit Name_ID #).