THat depends on whether you build it ELSA or EAB to a certain extent.
If you finish it ELSA, I'm not sure if you have to take a class to be able to maintain it, or if the fact that you built it allows you to. I know you can if you take the class.
If you finish it EAB, then technically you should list yourself and the original builder as builders, and technically the one who did the most qualifies for the Repairman's Certificate. Also, you need to demonstrate that the original builder and yourself built a major portion (the so-called "51% Rule") for your own education and/or recreation. Now, that's all technically speaking. In actual practice, most people in your situation would only list themselves as the builder when they register the plane, then they would probably be able to get the Repairman's Certificate upon showing their builder's log to a FSDO or MIDO (I'm not sure which or if both can issue it) rep. The easiest way I have seen to get this done is to go to the temporary FSDO at a show like Sun-N-Fun with your builder's log (take a lot of pictures of yourself building) and they can give you the Repairman's Certificate on the spot.