Death wobble is a condition that applies almost exclusively to Jeeps. Jeep owners coined the term, so they feel that it's their thing - and in a way they are correct. The recipe for a DW condition is essentially unique to Jeeps - think track bars used in conjunction with coil sprung front ends, solid front axle, short wheelbase and excessive lift.
It's not normally associated with 2WD pickup trucks. Let's see, you have the coil springs, but that's it. You don't have a track bar or a front axle - solid or otherwise. A short wheelbase isn't a problem with GM/Chevy pickups. Nor, from the looks of your avatar, is excessive lift.
The first thing to eliminate is the tires - and that doesn't just mean to check for uneven treadwear or an out of balance condition. There are some issues with tires that might be missed in a visual inspection and balancing. A broken radial belt - for example - will cause both of the problems you describe and isn't always readily apparent:
Some info on slipped radial belts that I cut and pasted when I was having an issue identical to yours with my van.
Steering
One of the primary functions of your tires is to help you steer the vehicle. The belts of the tire, especially the ones on the outsides of the tire, provide stability for the vehicle and allow it to turn as you instruct through the steering wheel. When the belts on the tire begin to slip, particularly the ones on the outer edges, you may find your vehicle is more difficult to steer. Your vehicle may adopt a tendency to pull one way or the other while the steering wheel remains straight. This can mimic the symptoms of a misaligned front-end or a dragging front brake.
Vibration
If the belts in your tires begin to slip, the wheels may be thrown out of balance. When tires are mounted on a vehicle, they are often balanced using metal weights to ensure that they roll without vibrating or wobbling. Despite the placement of these weights, a tire that has slipping belts may begin to vibrate. While this vibration does not have an impact on your ability to drive your vehicle, you can usually feel the vibration through your steering wheel. This sign is most significant at low speeds from 5 to 30 miles an hour and higher speeds from 50 to 70 miles an hour.
A couple of quick and easy checks for a slipped radial belt:
Sidewall Inspection
The belts in a radial tire extend across the entire tire from one side to the other. One purpose of these belts is to enhance the strength of the sidewall. When the belts begin to slip and pull apart, the sidewall weakens. This can cause the sidewalls to crack and visibly separate. You may also notice bulges in the side of the tire where it has more difficulty holding its shape. Larger tears may also occur in the sidewall.
Tread Inspection
In addition to checking the sidewalls of your tires, you should frequently inspect the treads to identify a potential problem. Check the tire for signs of cracking or separation in the treads. Look for signs of the steel threads showing through if you have steel-enforced radial tires. Monitor the treads for uneven wear. If a belt slips, it will create an odd shape to the tire that results in uneven wear based on the location of the slipped belt.
I'm sure you don't feel like eliminating the tires as the cause by going out and buying new ones - when yours look good. But if the vibration seems almost certain to be generated by something in the front end, try rotating the front tires to the rear and vice-versa. Drive around for awhile and if it is a tire issue, you'll probably be able to tell pretty quickly.
