Our Coupe (October 26, 1926) whether you call it a 26 or a 27 needs some parts painted I think. 1) What is correct for the radiator core and tanks? I was thinking flat black on the core and gloss on the tanks and sides. 2) Should the four wood toe boards be black or natural? 3) Should the wood floor board above the battery be black or natural? 4) Should the wood ceiling structure be natural, black or dark green?
Concerning the radiator, you need to use radiator paint. It is a very thin mist of black. Any paint on the radiator can interfere with heat conduction. If you are going to paint it, I would recommend you take it to a radiator shop for cleaning and let them paint it with the correct paint.
The closed cars all had carpet so floor boards were probably a wash black, the only wood in the top are the bows and the top rail which are unseen so most are natural wood as they are covered by the headliner. A picture of what you have would help.
If the Improved Car Coupe is like the 26-7 Tudor , the radiator was all on color: radiator paint black. From my experience, all the floorboard wood was painted the same color as the chassis; sort of a semi-gloss black. That goes for the battery access piece too. The ceiling structure was left natural as it was not exposed.
I'm sure that Kevin is correct. The radiator would not have been painted until the tanks were soldered to the core. Henry would not have gone to the trouble (and expense) of using two different types of paint.