How can I find a replacement external tub drain if the original has no identifiable markings?
Are you reinstalling a clawfoot or similar tub? Is this the overflow?  Was the bottom of the tub drain connected where the plastic fitting is?

Many vendors supply clawfoot tub reproduction plumbing.  The outlet sizes of the tub (both overflow and drain) determine the connections to be used.  The older clawfoots used 1 3/8 piping, the newer (and replacements, but check if its 100% reproduction) ones 1 1/2.