Three different products get mixed together here, so it's worth separating them.
Builder's risk (sometimes sold as a renovation or rehab policy) covers the structure and often the materials on site while work is being done, and it usually assumes the place is empty. A vacant property endorsement is an add-on to a regular policy that keeps coverage alive when nobody lives there, since most standard policies cut off or restrict coverage after a house sits empty for a set number of days. A landlord policy, often a dwelling fire form, is what covers the finished rented property, and it's the one that includes loss of rent.
The switch point isn't a calendar date, it's a condition. Most carriers want the property complete and either occupied or ready for occupancy. In practice operators call the agent when the work is signed off and the unit is rent-ready, and the agent binds the landlord policy to start that day so there's no gap. Ask your agent to put the trigger in writing, because what counts as complete differs by carrier and insurance rules vary by state.
Two things beyond your question. Carry liability coverage during the rehab and collect certificates of insurance from every contractor, because your builder's risk covers the building and does not make their crew's injuries your carrier's problem in the way you might assume. And when ledger says add the refinance lender as mortgagee, do it before closing rather than after, since the lender's closing checklist will ask for that certificate and a missing one delays funding.
