79 1 ton with the death wobble

[csb#356]

So I bought this 1979 K30 trailering special last night for 2500$. Drove perfect when I test drove it so I thought I was getting a smokin deal. Of course on the way home going down a steep bumpy downhill the death wobble starts. It only happens when i'm on the brakes with the combination of bumps, otherwise I can't get it to do it. All the steering seems tight, except the tilt column is sloppy. No up and down play on the wheels, and it doesn't look like there is any side to side play. Please give me any tips on things to check and I will look at them. Any help appreciated.