Oops. Didn't notice two cylinder engine at first.
Looks like a cassette type injection pump. There will be a linkage that goes back to it from the governor, so careful when (if) you pull it out. The timing is set by the shim, and fueling is controlled by the governor link. Throttle control pulls on a spring that affects the governor operation.
These pumps are still pretty simple. No timing issues. The only adjustment that is easy to get goofed up in a disassembly is cylinder balance. The fittings that come out to the lines probably have O rings, and Nitrile is a good idea if you pull them. There likely is a metal diaphragm that isolates the fuel from the oil and inside two pistons with metering barrels attached to a common link to control fueling.
Usually these setups are pretty hard to kill. Most likely problem is fuel is not getting TO the pump. They, like most (all?) IP's are not tolerant of water in the fuel. Algae sometimes can create some messy nightmares, too. If it is getting fuel TO the pump, and you are planning on replacing it anyway, I'd try and get inside it. Might be able to free it up and clean it out.
BEWARE of the little governor link. Usually there is a little clip that holds it on and it's pretty easy to drop into the case. I like to have a magnet probe hovering over it while removing it. If you pull the fittings below the injection lines, before pull the cassette assembly you will probably see immediately if there's been a water issue.
