Hello I will help you with your question,
I would get my insurance company involved to get a loaner and they can go after Toyota for the cost.
To date there has not been a recall issued but Toyota has recalled other vehicles for this problem. The 2013 Tundra will likely be added to the list in the future but it has not been yet.
I would file a report with the NHTSA and that will help speed the recall. In the meantime you are going to have to jump through Toyota's hoops until a recall is issued or they get high enough up the corporate ladder to issue you a check. Keep calm in your dealings with them and when you hit a wall just ask to see the district manage, the zone manager and the corporate manager so this gets escalated as soon as possible.
Please let m e know how I can help you with this