To get to the throttle linkage, you have to remove the right side cowling below the steering wheel. There are two bolts directly below the steering wheel and then you have to raise the hood and remove two more on the right side "firewall." Once removed, the cowling will lift out and away from the steering column. The left side comes out the same way, but you have two bolts to remove on that side before you can remove it and expose the relays.
As you remove the right-side cowling, be careful of the key switch electrical wires. With the cowling removed, you will see the toggle at the bottom of the throttle lever and the cable. Then you can troubleshoot why your lever is so wobbly.
As Danocheese mentioned, sometimes the throttle can freeze. I had that recently happen on my tractor and had to manually operate the throttle above the injection pump to get my tractor to stay running when I started it. Once it ran for a few minutes, the throttle cable thawed and everything was normal.
From your description, what I think is wrong with your tractor is the nut that holds the cable to the lever mechanism is probably loose or completely off your lever. I don't believe your problem is down by the injector pump.
EDIT: Here's an illustration of the lever.