If you haven't done it already, you can check the pump's action to some extent by disconnecting the fuel-supply line at the carb and turning the engine over with a starter.
You should get a fairly vigorous uninterrupted stream of fuel if all is well.
If you wish to dismantle the pump, it's quite a good idea to replace each of the four ?2mm bolts which go right through it from front to back, in turn, with a suitable length of wire,about 3" long,with a right-angle bend near the end of each wire.
Then you can "open" the pump out, with the components spread out along the wires, rather like a kebab, without too much risk of getting them out of order/alignment.
Edited to add:
If it's still the original rear bearing, even that new, the most likely material to block the pump is probably rust particles....