It's easy to test a mechanical fuel pump. Step 1 -- remove air cleaner, cycle throttle linkage while looking down carn throat. If it squirts gas, there is fuel in the flaot bowl and the accelerator pump (not "fuel" pump) is functioning.
If no squirt, it could be that the accelerator pump in the carb is dried out, or it could mean no fuel in the flaot bowl. Disconnect line from pump into carb and put the end into a glass jar. Have someone crank the engine (or use a remote starter switch). If the fuel pump is good, gas will flow out of the line into the jar. It should be a strong flow -- if it just dribbles, could be a clogged filter or could be a bad pump.