To see if it works...
On a cool morning in Los Altos (50F or so) the flapper should be closing off the main air intake from the radiator panel and open to the intake that is taking air off the exhaust manifold. Then heat up the intake with a hair dryer and the flapper should then start closing off the intake from the exhaust manifold and opening to the main air intake.
As Chris says, if it is not working you want it to fail with the main air intake open and the intake to the exhaust manifold closed. In Northern California that will be acceptable 90% of the time.
Mine works and it helps a lot here where sunny days in the winter it can still be only high 30s, low 40s.
I would not try to disassemble it for painting. Careful masking.