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A second home doesn't meet the IRS definition of a primary residence, it is not entitled to the capital gains exclusion. To qualify for the principal residence exclusion, you must pass the ownership and use tests. To pass the use test, you must have used the home as your primary residence for at least 730 days (24 months) in the five years immediately preceding the closing date of your home’s sale. If the taxpayer maintains more than one residence and divides their time on a seasonal basis between those residences, the dwelling in which they spend more time would qualify as their principal residence. Other types of proof may be required to establish where one’s principal residence is. This can include utility bills with the occupant’s name and address, a driver’s license with the address, or a voter registration card.
With this being said, if you've owned your second home for more than a year, you'll typically pay a long-term capital gains tax between 0% and 20%, depending on your earnings.
IRS resource link: https://www.irs.gov/faqs/capital-gains-losses-and-sale-of-home/property-basis-sale-of-home-etc/property-basis-sale-of-home-etc-6
