Sudden cut-out

So I've been working through some issues with my '76 SN, most attributed to just old gas and some carb tweeking. But the last nagging issue I'm having is that about 1/2 the time when I put it into gear and push the throttle down, the boat just shuts off. I used to think that was related to the other probs I was having, but now I have the boat starting right up, idling well, and running well for a blast across the lake- when I can get it off the dock.

I'm thinking that the sudden shut off may be related to the neutral safety switch. Is this plausible? Has anyone seen where the safety switch at the throttle handle would cut out the ignition under normal operation? I've noticed that once in a while the ignition is completely dead- no clicking, slow turning, etc- but after a little fussing around in the drivers seat, she'll turn over and start right up. Thinking that these may be related.

When you push the throttle do you get a good shot of gas out of the accelerator pump nozzles?

You can check this with the engine Off.

Disconnect the throttle cable at the carburetor and you can move the throttle linkage and look down the primary bores (with the choke open) and you should see a good shot of gas into each primary venturi.

If it starts right up (assuming you give it a couple of pumps of the throttle to start it) the accelerator pump is probably working, but you want to verify that the squirt of gas starts as soon as the linkage is moved

Like Pete said the NSS won't come into play with the engine already running