The mortgage gets the attention on this site because it's the biggest amortized loan most people carry. But the mechanics don't care what the debt is. They need a revolving line of credit with daily interest to park in, and an amortized loan with front-loaded interest to chunk at. Renters have both, in smaller sizes.
The line of credit is the harder part. Without home equity there's no HELOC, so the tool is a personal line of credit, usually from a credit union. It's unsecured, the limit is smaller, and the rate is higher, sometimes by a lot. That matters less than it sounds, because the balance in a parking plan spends most of the month low, and interest is charged on the average daily balance, not the limit. A share-secured line, backed by money in a savings account at the same credit union, is the cheapest version and the easiest approval. The choice between the types is in HELOC or personal line of credit.
The chunking target is whatever amortized loan carries the most interest. For a lot of renters that's the car loan, then a student loan. Both front-load interest the way a mortgage does, on a shorter clock. Take a $31,000 car loan at 7% over 72 months. A $4,000 chunk at the one-year mark moves the payoff date forward by ten months, and the payback to the line of credit runs through the sweep the same way it would for a homeowner.
Rent itself can't be chunked. There's no principal in it. What the plan does for rent is timing: rent goes out of the line of credit on the first, the paycheck lands on the fifteenth, and the interest on that gap is small because the gap is short. The real gain is that the surplus you find each month has somewhere to go that isn't checking, where it usually evaporates by the 28th.
Unsecured lines come with two risks a HELOC doesn't. The lender can reduce or close one faster than a HELOC, because there's no collateral holding them to it, so keep the balance well under the limit and never treat the room as your only emergency fund. And personal lines sometimes carry annual or inactivity fees that make a small line of credit expensive, so read the fee sheet.
The bigger reason to start this as a renter is the down payment. A household that has run the sweep for two years knows its real monthly surplus to the dollar, has a revolving line of credit in good standing on its credit report, and routes money deliberately. That's the household that gets the mortgage approved, and the one that starts chunking it the month after closing. Open the personal line of credit, park one paycheck, and run the first chunk at the car loan before the year is out.