According to IRS Publication 587 Business Use of Your Home, only daycare providers can use the percentage by time for business use of the home percentage (along with the square footage percentage). Other lines of business can only use the square footage percentage based on the portion of the home used exclusively and regularly for business.
If your home office is only used a portion of the time to generate your income (and otherwise used for personal purposes), according to the instructions in this publication, it would not be eligible for a deduction as it is not used exclusively for your business.
Per IRS Publication 587 Business Use of Your Home (Including Use by Daycare Providers), page 3:
Qualifying for a Deduction
Generally, you cannot deduct items related to your home, such as mortgage interest, real estate taxes, utilities, maintenance, rent, depreciation, or property insurance, as business expenses. However, you may be able to deduct expenses related to the business use of part of your home if you meet specific requirements. Even then, the deductible amount of these types of expenses may be limited. Use this section and Figure A to decide if you can deduct expenses for the business use of your home.
To qualify to deduct expenses for business use of your home, you must use part of your home:
You may want to consider setting up an area in your home that would meet the definitions of "exclusive and regular" use for your business according to the publication so you could deem that as your home office. As mentioned in the publication, the area can be a room or other separately identifiable space and does not need to be marked off by a permanent partition.