Pop the enquiry off to Gretsch in an email or contact form on their website for a definitive answer.

Not first hand famil with that particular instrument's finish. Does the body paintwork have a topcoat of Matt or Satin Polyurethane Clear? Or is it open pore?

If the former, the surface is sealed (colour coat is protected) and Lemon Oil won't penetrate the paint work or affect the hard poly coat. Same could reasonably be assumed with Dunlop's Polish. For point of reference, I have and use the full range of Dunlop maintenance products. If in any doubt about the body being clear polyurethane topcoated, don't, or test on a small obscure area first.

Alternatively, you'd be safe with Ernie Ball liquid instrument polish (spray). Non-abrasive with no cutting constituent, it does a great job cleaning grime. I use it on open pore stained instruments as well with no ill effect.