If you purchase an Experimental category aircraft you can do the work on the aircraft but the work must be signed off by a licensed mechanic. (A&P) If you (and any number of your closest friends)do 51% of the work on an Experimental Amateur Built aircraft you (or any one of those friends as long as they were not paid) may apply for the repairman's certificate for that airplane. The certificate is not good for any other aircraft even if that aircraft is identical in every way.

Like you I am a little foggy on some of the wording in the Light Sport arena but if the term Experimental is attached I would bet the above applies.