I have to guess which boat you have, engine serial number and year are necessary when ordering parts and performing service.
However, they all work essentially the same, thus on the end of the jet pump you'll find a cable-controlled reverse gate (aka reverse bucket) that moves up and down as the cable core wire moves in and out of the transom. The cable outer sheath is bulkhead mounted to the transom and the inner core wire of the cable connected to the bucket moves in and out, which in turn moves the bucket up and down accordingly.
Easy stuff first......
The cable core wire is connected to the reverse gate lever arm using a bolt through a ball link clevis, so remove that bolt and check to see if the gate moves freely. If the gate isn't binding as you move it up and down while the cab;e is disconnected, this suggests the gate is free to move.
While there, inspect the clevis itself for damage, it might be bent or something.
The other end of the cable outer sheath is mounted to the shifter housing up at the helm, and the inner core wire is attached to the shift lever that moves fore and aft.
Crawl up in there and disconnect the inner core wire clevis from the shifter arm, probably held by a cotter pin through a connector pin. Remove the cotter pin and slide the connector pin, which disconnects the core wire from the shifter lever.
Then carefully, so as not to cause damage to the disconnected core wire (you might need to hold it away from the shifter arm), test to see how much effort is necessary to move the shifter. Assuming the shifter moves fore and aft with normal pressure, try by hand, to move the core wire in and out of the cable sheath.
I'd almost bet the core wire is very difficult to slide in and out of the cable outer sheath, which shouldn't be the case. You should be able, with minimum effort, to slide the inner core wire in and out of the outer sheath.
I should mention that depending on the details of how the boat was constructed, it might be necessary for you to remove the shifter mechanism from it's mounting location in order to disconnect the inner core wire from the shift arm. Many boats the shifter is not accessible from under the helm.
I pulled new steering ans shift cables through a Four Winns twin screw Volvo Penta just last week, shifts like a breeze and steers great, now. It's very common for the inner core wires to begin binding while sliding through the outer sheath after just a few years, depending on weather and environment.
So assuming your cable is shot, you'll need a replacement and it will be necessary to fully disconnect both ends completely so you an pull the old cab;e out and snake the new one back in.
In many cases, there will be a few plastic tie-wraps holding the cable along it's length you'll need to cut in order to free it up but you might also be able to attach the endof the new cable to the old cable and pull the new one trhough without much hassle. Using this method can save a lot of time and effort crawling through the bilge and reaching up under the deck from below. Also, the factory routing is preserved (important, IMO).
Good luck, it's not really that difficult. Just time consuming like anything else don't rush it. You'll need an assortment of tools of course, which varies depending on the detail of how the boat was constructed. Don't forget to replace any plastic tie-wraps you had to cut while freeing the cable and snaking the new one back in place.
