05 tundra steering wheel shake

Hey guys, just bought an 05 tundra access cab limited trd off road 4x4 with 92000. It had a shake in the steering wheel at about 65-70 mph when I test drove it. The guy had the tires balanced and it seems better but still has a small side to side shake at 60 to 70 mph.
Any ideas on what could be causing this? It has wrangler all terrain tires. The truck was parked for a month. Any thoughts appreciated. I had an 06 tundra before with a similar problem years ago and think I remember something about the tires having to be balanced on the inside and out?

 

See if you can take it to a place that does "Road Force" check and Balancing. Could be a bad tire, or just a bad balance. There are practices that can net a better balance depending on the tools used.

 

What he said ^^

 

Mine are the same way and I swear it's not even consistent. Could be the road but idk. What is a "road force" balance.

 

^^ x3. I had that exact same issue until I had a balance and rotate done to the tires, it completely went away.

 

A road force check, checks for uneven pressure in the tire/wheel assembly. Uneven pressure could be caused by bent wheel or our of round tire (visual inspection might catch those), it could also catch uneven belt lay down or separating of belts (tire carcass damage).

 

X3. I rotated and balanced mine, problem gone. The issue on a lot of these rigs is aggressive, block-type tire tread, vs the more sedate ribbed 'street' tire tread. As block tread tires wear, they cup, especially on the shoulders of the tires, and this causes wheel shimmy. I rotate block tread tires at every oil change to keep them round as long as possible!