Does basic training count as still living at home?

You lost the child tax credit when the child turned 17.    After they turn 17 you get the $500 credit for other dependents, which is a non-refundable credit that can reduce your tax owed.   You have not mentioned the child's age or how much they earned in 2024.

IRS interview to help determine who can be claimed:

https://www.irs.gov/help/ita/who-can-i-claim-as-a-dependent

Q. Does basic training count as still living at home?

A. Yes. Time in basic (and advanced) training is considered as only a temporary absence from your home) for purposes of claiming the child as a Qualifying Child dependent.  It does not get you the child tax credit, if he is over 16 (as most military are), only the $500 other dependent credit and maybe some EIC.

There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit. They are interrelated but the rules are different for each.

The support test is different for each type. The support test, for a QC, is only that the child didn't provide more than half his own support. The support test for a Qualifying Relative is that the taxpayer provided more than half the relative's support.

A child of a taxpayer can still be a “Qualifying Child” (QC) dependent, regardless of his/her income, if:

1. He is under age 19, or under 24 if a full time student for at least 5 months of the year, or is totally & permanently disabled
2. He did not provide more than 1/2 his own support. Scholarships are excluded from the support calculation
3. He lived with the parent (including temporary absences such as away at school or military training) for more than half the year