For the European delivered W113 for German market, you can purchase, if still made available from Mercedes-Benz Classic Center USA, the Classic Mercedes-Benz Certificate (Zertifikat). This document will give you the "Destination of Delivery", such in my case was Mercedes-Benz Reulingen branch, West Germany. Then you will know the city/town, and you can start your research there to locate the car's history of ownership with the state office (Kraftfahrt Bundesamt) for car registration. I was lucky in that the German owners (2, a medical doctor and a music conductor) passed the Kraftfahrzeugbrief document when car was sold to the person I bought the car from. This Kraftfahrzeugbrief, has information as to the names of owners, addresses, dates purchased, even has the different license plate numbers used during it's life in Germany. Side note, the last trip I took to Germany, two years ago, I even contacted the last German owner of my SL, the music conductor. He was so surprised to find the car still on the road and in America. The frist owner, the doctor had pasted away. I still today write to the conductor about the current life of the SL.
Yes, Richard is correct, the Data Card also gives you information as to the Auftrags Nr. (the order number - 8 digits - the first digit is the last digit of the year in which order was placed, the next three digits identify the region, if in Germany the Niederlass Ungen (MB Company owned dealerships/branch, or country, if not Germany, from which order was placed, next four digits are the sequential order by region/country/year. Good luck in your search. If your W113 was a USA delivery, you might have a harder time tracing the history. I think the fun in ownership of these classics is the search. You know, the search to find a W113 to buy, the search to find parts for restorations, the search for a highly qualified mechanic, the search for the best roads to travel these cars on, the search for the individual history of you car, and in some cases for those that are unhappy with theirs, the search for a buyer.
Bob