No rent and used by a relative - You and your sibling have a "2nd home". As such, the mortgage interest and real estate taxes are deductible as itemized deductions. The mortgage interest is not subject to investment interest limitations. Property tax is subject to the $10K limit on deducting SALT (state and local taxes). You would each deduct what you actually pay. No business (schedule C) or rental losses (Schedule E) are allowed. No deduction for HOA fees, depreciation, repairs and maintenance or utilities is allowed.
"Gift Tax" is somewhat of a misnomer. Even though a gift tax return may be required, very few people ever actually pay federal gift tax. The purpose of the gift tax return is usually only to document a reduction in the allowable estate tax exemption.
See https://turbotax.intuit.com/tax-tools/tax-tips/Tax-Planning-and-Checklists/The-Gift-Tax-Made-Simple/...
