Front end shimmy

This is weird, when I tow something light like a jetski the truck feels like it shakes or shimmys just a little bit upon take off everytime. This is a brand new problem as the truck didnt used to do that, everything including the wheels are standard...its a 2005 Tacoma prerunner, anyone know what this problem could be?

 

If you have a carrier bearing, check that, then the driveshaft u-joints.

 

I agree, the diveline angles can change when towing.
That is one of the reasons you have a slip joint.

 

Simply put Tacomas stock rear springs are too soft so as soon as you put any weight on the rear as payload or towing the rear pinon angle changes relative to the trans/xfer angle as the springs wrap on take off. Many pots on site related to all this.