Can't provide a direct answer since our Corolla is 2006 and 5-speed. More to the point, it doesn't have a navigation screen and such extras.
What I can say, is that we didn't have problems with Brake Buddy (first the Classic, now the Vantage Select) running the battery down, in any of the four basic toads we've had. Each has been upgraded once: Tercel ==> Corolla, then Mighty Max Pickup ==> Frontier. We usually reach a destination within a day, and our trips don't usually require much braking en-route.
For Toyota's part in this, instructions are on Page 171
HERE. All they say is to turn the KEY to ACC, and any Accessories OFF.
Toyota, of course, doesn't know you're going to power a Brake Buddy or similar device from their Battery. This tip won't affect Battery Life, but it WILL help Brake Buddy Performance: You'll have to run wire into the Cabin for the Breakaway Switch that's provided with a BB unit. CALL BB and talk to a tech about their "12-Volt Direct Battery Kit."
You can order it for $20 but Tech Support will probably mail you one for free. They brought this out because cars now have "utility outlets" where they used to have "lighters" and the outlets are served by skinny wire with small fuses. The Kit doesn't look like this picture any more. You get an ATO "Blade" fuse with holder, and the Socket is Metal. FAR more reliable than the pictured one.
Anyhow, power your BB direct from the Battery with that Kit for MUCH better operation and reliability.
Another good thing about the Kit, it allows you to install a Battery Disconnect as part of the car manufacturer's instructions, and still power a BB. Kit can be installed in a way that the Socket stays HOT with the Disconnect turned to OFF.
