As long as it was available to be rented during that time, you can claim rental expenses. If it was listed for only 240 days of the year, the remainer is not necessarily personal use.
According to IRS Pub 527 - Vacant Property:
If you hold property for rental purposes, you may be able to deduct your ordinary and necessary expenses (including depreciation) for managing, conserving, or maintaining the property while the property is vacant.
Personal Use Days are any days that you used the rental space during the period it was available to be rented.
If you did not personally occupy the space while it was rented, you would enter zero personal use days.
See the examples here: IRS Pub 527 What is a day of personal use? and the later discussion of days used for maintenance.
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