The answer to this question is totally personal because my writing, like the writing of every author, is personal.
It wouldn’t make any difference in my character as long as I hadn’t already begun writing because, once I had the gender assigned, I’d proceed with the subconscious awareness of the character’s gender and that would show in the finished product.
However, there’s a caveat to this subject: if an author departs from acceptable gender stereotypes/archetypes/behaviors, then he/she had better do a good job of explaining why that particular character doesn’t behave as most characters of his/her gender do.
Because readers have certain expectations of gender-assigned behavior. They are normally fine with outliers as long as the reasons for those outliers are made clear. But they will descend upon the author with their claws sharpened if the character does not behave as expected with no explanation given.