I would think it would be dependent upon the amount of vacuum made from the source.
I thought, just by reading this site, that '67 RS's only had vacuum mechanisms.
My thoughts are these, the door assy with the least resistance in movement will move first, when that's done, the other door will open.
Could be the camshaft is other than stock, vacuum gauge should show between 18-21 inches of vacuum. The bigger the cam, the less vacuum. Or maybe the source is from the wrong place, an intake runner rather than the plenun under the carb.
You could always hook up an 20-30 gal air tank to an A/C vacuum pump and hook the supply hose to the door assys for troubleshooting rather than waste gas from the engine.