Upvote:7
The question as currently posed isn't directly answerable because it is based on overly simplistic assumptions about how genetics work.
The presence of red hair doesn't always indicate the presence of a specific gene or vice versa. About 80% of people with red hair have a variant of MC1R, the so-called "ginger gene". This gene is much older than humans and regulates pigmentation in a wide range of other mammals. It is also important to understand that there are many variants of this gene which may or may not be associated with red hair.
At the level of haplogroups and subclades rather than any particular gene, we can infer complex patterns of population mixture in Europe over recent centuries. Here's an interesting map of how haplogroups are thought to have moved through Europe over time:
In sum "the ginger gene" definitely did not originate in the Celtic or Nordic region and then move from one to the other. Specific variations of it inhereted from Germanic populations may have become more prevelant over time, but if so, this would have happened indepently in each of the two areas.