From Delta Whiskey:
RV9ralph - I'll have to admit that your comment "The owner has to sign off the work" sent me off into the vastness of the internet and I learned a lot about a bunch of similar or related questions but not this one specifically.
Like you, I cannot refer to a specific section of the FARs. My statement was based on information I have gathered over the years talking to A&Ps, IAs, articles I have read, conversations I have had and presentations at EAA meetings by FAA FSDO reps.

The concern here is who can do work and sign off for work on an E-AB aircraft. By my experience through the above sources is that the owner can do any work on the E-AB certificated aircraft (except sign off the Condition Inspection unless being the holder of a Repairman Certificate for that specific aircraft). The FARs do specify that there must be a record kept of that work and the person signing off that work must enter their certificate number. In the case of the owner, that would be their pilot certificate. If work is done by a non certificated person, that work should be done under the supervision of the person returning the aircraft to service and the signature would be the owner. Operating Limitations issued for specific aircraft may outline this depending on when they were issued.

However, I will state that anything I have written may be challenged by anyone and different FSDOs will interpret things as they wish. Just try to stay as informed as possible.