Most obvious if it's that old it will have the Rocket Lugs.

Here is a link to a paper about the different round badges and approximate eras when they were used. http://www.gretschdrumdatingguide.com/other-gretsch-projects.html

This should get you in the ballpark, along with changes in hardware like lugs as KO mentions. You might look for the type of tone control (single round felt with horizontal mount bolts are earlier than the two rectangular felts type with a single mount hole) or hoops (straight hoops that required clips spanned a long time, but are genrerally earlier, non-die cast hoops with holes for the tension rods came next, die cast came later). Interior paint started in about 1954. If earlier and unpainted, it may have a date stamp which would answer your age question.

That's an interesting series of pictures, but I don't see any dates except for the very first picture. It doesn't say whether they are arranged chronologically? Do you have dates to attach to the other pictures?

One other thing not yet mentioned, is that the earlier drums (up to 52?) often had date stamps inside, if you're able to take a head off.

But frankly, I'm not sure the age matters that much as far as value? i.e. it isn't necessarily true that the older the better. I would base it more on throwoff type and number of lugs. Best (and out of the park) would be a Gladstone throw; next would be a working Microsensitive; next would be a three pt throw, then finally a four pt throw. Eight lugs definitely better than six.

There is a paper that is reached by clicking on the link at that site. That paper contains the approximate dates of use for each badge. A number of examples of the different badges were gathered. I believe that each can be separated into the general time frames when they were used based upon date stamps and hardware chages. Like many things with vintage drums, precise start and stop dates are difficult to establish.