The real explanation is much simpler (and less interesting) than some offered above.
You learn dactylonomy—finger-counting—when you're an infant, and you don't re-learn it as an adult unless there's a good reason to do so. It doesn't matter how thoroughly a British person immerses himself in a Continental culture, or vice versa, he/she is unlikely (and has no need) to switch dactylonomic codes, especially when the two systems are mutually intelligible.
Little Archie Hickox learned to count with his fingers on the knee of his Irish mother or father, who passed the art on, unchanged, from their own infancy, und so weiter, und so weiter.
As soon as you can do basic arithmetic, finger-counting becomes pretty irrelevant to your life, unless you order a lot of beers or work with a lot of trauma patients. You could theoretically go your whole adult life without ever counting on your fingers...
...until you have kids of your own. Then you enact the same, indelibly-rehearsed motor actions your parents instilled in you.
As a young man, Archibald Hickox' interest in German probably caused him to spend no end of time among no shortage of native speakers.
He could have spent 1000 years in the company of his echt German friends; it would have helped him shake off the Irish accent, to be sure, but it probably wouldn't have had any influence on his dactylonomic habits. After all:
- he was hanging out with them to improve his German
- he already knew how to count on his fingers
- nobody at his Ye Olde Bavarian Beer Hall, be they echt Bavarians or just students dressed up in Lederhosen und so weiter, ever seemed to have difficulty understanding how many glasses he wanted when he signaled for zwei, drei, vier or fünf Gläser*. Even in Occupied France his gestures worked fine: note that, just before Hellstrom leveled a pistol at Hickox' Eier, the bartender delivered exactly 3 glasses to the table.
The ScheiBe hit the fan because Hickox violated what linguists call an ethonomathematical shibboleth.
Unfortunately Hickox was a film critic, not a professional spy. Any espionage instructor worth her salt would have drilled Hickox on the life-or-death importance of dactylonomic and other shibboleths, particularly because these are somewhat quicker and easier to master than a clean foreign accent.
But you have to know that you HAVE to master them. And we can't expect someone who's not a professional spy to have thought of these things.