IIRC, according to Roger Freeman 8th Air Force
fighters were never
officially instructed to 'tone down' their national insignias as IIRC the bomber groups
were. Going on memory here. Makes sense from the start as the bombers were lumbering along and the insignias (they must have figured out back then) were nice aiming points for the Luftwaffe.
However, there are examples where it's pretty obvious (including good clear shots of obvious no-masking tape paint overspray on the insignia) that "toning down" did indeed occur in some 8AF fighter groups and/or squadrons.
The 'irony' of 8th AF markings for artists like me and my friends in the serious scale modelling community is that while the 8th is so well documented in terms of photos and
official general markings regulations/guidelines, there was a tremendous latitude in the time periods of application/adherence to regs of markings application group to group, and even squadron to squadron.
In some groups, the squadron commanders were the "gods" of their units, with much leeway in less-important areas like this. In other groups, the burning bush resided in the group commander's office alone. I suspect personalities had much to do with each case-by-case basis. The evidence suggests that if a group was "hot" and pulled their fair share and then some, VIII Fighter Command, especially in the Doolittle/Kepner era, didn't sweat the small stuff like whether or not a squadron sprayed some gray on their insignias a'la what the bomber boys were doing.
That's why I specialize in the 8th ... every time I begin research for a painting I have to start from scratch almost and figure out what squadron "X" was doing to their planes as of the date of my planned painting - luckily, as I said, while there were differences group to group and even squadron to squadron, the 8th was so well covered image-wise that the detective work is made much easier.
And thanks to guys like Jack and Martin who always seem to have one or two magic images to illustrate (or discredit

) certain points ... guys? ...
Wade