If there"s continuity, but no voltage at the neutral safety switch, then there"s a problem with that circuitry. One side of the switch has to show voltage when the keyswitch is on & the rotary switch on the dash is turned to start.
One time I had "no starter" on the 5040 but it wasnt the starter itself. The problem was a bit different than you describe.... the neutral safety switch was not making contact. It was easy to find as I just jumped across the terminals with a screwdriver, turned the rotary switch and it started.
The switch is a crimp-sealed unit. I was able to get it apart and found corroded contacts inside. Cleaned the contacts and put it back together"; no problems since. But, it was a bit of a chore to alter the case to get it back together without the crimp.
However, I"d suggest double checking that neutral safety switch by temporarilly bypassing it. If that works, the switch is bad or corroded inside.