In case anyone else stumbles across this. This sequence of blinks signifies the device is shutting down/ powering off. I ended up trying a different charger, as well as attempting to charge through thunderbolt, which gave slightly different behavior. Seemed as though it was charging (would give a solid orange light for a few seconds) and then give this set of blinks again.
I was unable to find the exact fault in this case, I have much less experience with PC board troubleshooting, but since the unit was under warranty I replaced the system board, which resolved the issue.