A second home that you used for personal purposes (i.e., not as a rental property) is a personal asset. As such, loss on the sale of a second home is not tax deductible. However, if you received Form 1099-S, Proceeds from Real Estate Transactions, you should report the transaction on Form 8949 and Schedule D because IRS computers will be looking for your reporting. In column (f) of Form 8949, you should enter adjustment code L to indicate you have the nondeductible loss and enter the amount in column (g), so no gain or loss is shown on the transaction in column (h).
Intangible assets that come within Section 197, such as goodwill, are amortizable over a 15-year period.