Yes, the 3208 fuel transfer pump (lift pump) is built into the very front of the 3208 injection pump itself. 

Most people just replace the entire 3208 fuel injection pump and governor unit with a CAT reman injection pump and governor.


Why? 

Once removed, you have to also pull the rear 3208 governor and "hold fuel injection pump's camshaft totally forward" BEFORE you pull the CAT 3208 front fuel transfer pump, OR the camshaft's thrust washer "tab/tang" fails out of its notch, and requires almost a total disassembly of that old injection pump and governor, to get tang/tab back into the cast iron housing notch.

Also, the lip seal area, for transfer pump seal, tends to wear a groove into camshaft's front snout. (that would be a new surface, if you buy a CAT reman; so you don't need to worry about an improper sealing surface, if you try to repair an old injection pump, that probably has a groove worn in it.)

Also, again; once you have the rear 3208 governor off, you might need to ream/rebush/reseal the throttle shaft linkage, too. (They tend to "suck air" in that location, also)

Also, in your case, maybe the internal fuel injection pump's linkage that controls the 8 sleeve metering collars, might be "hanging up" and not allowing fuel to be squirted into the fuel nozzles (won't create the high fuel pressure) Even though the electric shutoff solenoid is working.


Plenty of reasons, to just step-up to a Reman injection pump and governor, if you might have a couple of these issues, already going on , in a particular 3208 injection/governor pump unit. 

I need to go combine and haul corn , won't be back until late, tonight.