You have to come up with a method to prorate (or allocate) the income. The method must be reasonable. If your employer has a record of your job tickets, you may be able to use that information to differentiate between the work in the two states. Document whatever method you do use, in case Idaho questions it.
But you are correct for allocating: Washington has no state tax, and as a Washington resident, you aren't taxed by Idaho for work you do in Washington.
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