However, unlike the description of the gifted child, my son really appears emotionless in most situations. I know, as his mother, that he internalizes a lot of emotions. I have to talk at length with him about emotional situations to get him to "feel" (for example, the death of his grandfather this year).
Someone in your school district is in charge of the gifted program. I recommend that you contact the school district office and ask who that person is. There should also be a printed description in your school district office outlining the criteria for entering into the gifted program. Do not feel that you are "pushing," you are only seeking what is essentially public information about an educational program. I suggest you move quickly on this, as most placement decisions are made in the spring term for the following school year. If intelligence testing is required, due to time constraints, you may have to pay for outside-of-school testing.
Regarding the emotionality issue, your son may be more amenable to discussing other people's emotions rather than his own. Try this approach: Since your little guy admires Lincoln, you could bring up how sad Lincoln must have been when he lost his young son Tad. Also, does your son's father easily discuss his feelings? A male role model who shows it's okay to be expressive does wonders for a young boy.