There are different rules for different tax benefits.
To be eligible for the child tax credit, the person must be your dependent AND age 16 or less (age 17 or less for 2021 only).
To be eligible for EIC (and qualify you for head of household) the person must live in your home more than half the year, AND be under age 19 or under age 24 while also a full time student or permanently disabled. The child can qualify for EIC even if they are too old to get the child tax credit.
However, you must be aware of the definition of "permanently disabled." For income tax purposes, disabled means unable to perform substantial gainful work. Many people who would be considered medically disabled (blind, paraplegic, etc) can still perform gainful work and are not disabled for income tax purposes. If the child can work a "regular" job for at least minimum wage without or with only minor accommodations, they are considered to be able to perform gainful work and will not be considered disabled for tax purposes. So it really depends on the degree of disability and the capabilities of each individual.
Here is an IRS information sheet.
https://www.irs.gov/pub/irs-pdf/p3966.pdf
