I would replace the bearing(s). Too much play in the bearings allowing the axles to wobble is one of the reasons why the rear axle seal fails. Your Tundra doesn't have a million miles and hasn't been abused, so stuff like flexing of the housing doesn't make a lot of sense. OTOH my axle was still running the bearings that Toyota put in up until a couple of years ago, so anything's possible.
'91 Pickup - Imelda / '08 Tacoma TRD - Donna
'09 Kawasaki KLR650
'98 Rhygin Juke SS / '12 Gunnar Rockhound 29 / '16 REEB Dikyelous
"Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty. Nobody is able to achieve this completely, but the striving for such achievement is in itself a part of the liberation and a foundation for inner security. " --Albert Einstein