Short version:
I suspect one cable is binding, maybe the wire part split within the sheath, and is preventing the other from moving the lever. Keep in mind that, for one cable to move the throttle lever, the throttle lever needs to be able to move the other cable.
Worse, if you push it you may end up breaking the good cable, because the roce is going somewhere.
What you want to do is disconnect both at the pump end and see which one is moving and which one is stuck and go from there to figure out if the stuck one is stuck within the control or within the cable.
Happy huntin!
Long version:
I'd take it one step at a time.
1) Arrange for a helper to go to each of the helms when asked. Call them when you need them "in a few minutes".
2) Go down to/into the engine compartment, to the affected engine, and where you good access to the injector pump and the associated ends of the problematic throttle control cables.
3) Disconnect everything at the injector pump throttle lever. Ensure that each cable end is free and that the throttle lever is free of any cable mounting hardware.
4) Attempt to exercise the throttle lever on the injector pump. Does the throttle lever at the injector pump move freely and smoothly?
5) Call your helper via your cell phone and send them to one of the helm throttle controls. Stay on the phone with them to be able to communicate.
6) Once your helper is at one of the helms, hold both control cables in your hand such that cable can move freely and such that you can watch the end move in and out. Have your helper slowly exercise the throttle letting you know which direction they are moving it in. It should move smoothly and without unreasonable force at their end. Have them stop and communicate with you if this is not the case. At your end, you should see one of the two cable ends in your hand move as they move the control. If they encounter unusual resistance or you don't see movement in the cable corresponding to the movement of the control, you've found a problem.
7) Have them go to the other helm and repeat the experiment.
8) I suspect you'll find that one of the two cables is binding and you'll soon see that the binding cable is what was preventing the other cable and the throttle lever on the pump from moving.
9a) If my suspicion is correct, connect the working cable directly to the throttle lever of the pump if possible. If not possible, reinstall whatever of the intermediate links/hardware need to be reinstalled first and then make the connection-- but do not reattach the cable that didn't work properly, just the one that did.
10a) Continuing under the assumption that my suspicion was correct, have your helper again exercise the control that appeared to be working and has been reattached. I suspect you'll find that it now works correctly. Congratulations! You've isolated the problem to the other cable/control.
11a) Go to the misbehaving control and disconnect the cable from it, entirely.
12a) Go back down to the engine and again hold the loose, now suspect, cable in your hand so you can see the end.
13a) Have your helper slowly push and pull the cable through its full motion manually by the end (still on a cell call, still stopping if it doesn't move well, and still describing what they are doing to you). I suspect you'll see it doesn't move as it should. Congratulations. You've isolated the bad cable.
14a) If the cable did work smoothly, go back up to the control and examine it carefully. Operate it and watch the motions. I suspect you'll observe a problem. Congratulations, you found a bad control.
15a) If the cable worked manually, but didn't work via the control, and the control looks good, check the cable sheath near the control very carefully. It is probable cracked or damaged or squeezed by the clamp. If not, it is probably split within a few feet of the control. If this is the case, congratulations, you've isolated a bad cable.
16a) If you haven't yet found the problem, have your helper bend the cable to simulate how it bends as it normally goes to the control and repeat the manual movement experiment. If it binds, congratulations, you found a bad cable. The wires are split inside and bind when it is bend. If the problem doesn't appear, bend it some more, over bend it a little bit, and check again. If the problem appears, congratulations, you found a bad cable.
17a) If you haven't yet found the problem, repeat the exercises above, except at the pump end. Look carefully for splits and sheath damage, then bend it near the injector pump and have your helper try again. If you find damage or it binds, congratulations, you isolated a bad cable.
18a) If both cables test good, and the control looks good, reassemble install the cables into the control again. Check carefully for interference, e.g. a screw that backed out, between the clamp and where the control moves the wire part of the cable.
19a) Of course, you could in theory have a bad cable and a bad control and an interference problem. So, finding one doesn't guarantee there won't be another problem. But, I'd assume only the 1st problem you find until you fix it and then another turns up...
9b) If my suspicion in (8) was wrong and you found both of the cables binding, congratulations. You got lucky and had two failures at the same time. Repeat the (a) path above for each of them to isolate each to a control, or a cable, or possibly even both -- you could, in theory, get double or triple "lucky".
9c) If neither of the cables is binding, repeat the (a) path above for each to see at what point the problem reappears. Pay particular attention for any physical interference from the clamps to the pump.
Happy hunting!
