Fly the Runway Heading
From the Pilot Controller Glossary and Instrument Procedures Handbook:
Runway Heading
The magnetic direction that corresponds with the runway centerline extended, not the painted runway numbers on the runway. Pilots cleared to “fly or maintain runway heading” are expected to fly or maintain the published heading that corresponds with the extended centerline of the departure runway (until otherwise instructed by ATC), and are not to apply drift correction; e.g., RWY 4, actual magnetic heading of the runway centerline 044.22°, fly 044°.
I knew we aren’t supposed to apply drift correction when flying headings, but I didn’t know we were supposed to fly the actual runway heading not the runway number.