http://www.correctcraftfan.com/downloads/Velvet_Drive_71C-72C_Transmission_Service_Manual.pdf" rel="nofollow - link

Look at page 9 and it'll show an arrow pointing to the Neutral Safety Switch.

Since you have to do "the jiggle", there's a good chance ( like really good) that your present switch is good, and your cable needs adjustment and/or has worn cable ends either at the transmission or at the throttle/shifter control.

They should get looked at for wear/slop before just replacing the switch 

Here's a link to a thread about cable adjustment

http://www.correctcraftfan.com/forum/forum_posts.asp?TID=26601&title=shift-cable-adjustment-pcm-123-and-morse" rel="nofollow - link

http://www.correctcraftfan.com/forum/forum_posts.asp?TID=43116&title=bad-shift-cable-or-control" rel="nofollow - link

With some wear on the cable ends, the jiggle works till there's too much wear or one breaks completely

If the shifter is in Neutral, what should I look for on the Transmission to make sure it is positioned correctly?  

It's not easy to get at the one on the back of the throttle  but it can be the culprit.

Working half blind, upside down in a tight space or removing the whole assembly from it mounting in the gunwale are the choices.

I'd get a look back behind the throttle with a light and mirror or take a couple of pictures that you can blow up to give yourself an idea of the condition of the connector and the one for the throttle too that's back there.

Glad to keep your mind sharp 

To me slop at one end of the cable isn't any different than slop at the other end. Either end affects that direct connection between the local arm and the throttle control arm and affects your once smooth consistent shifting............to me maybe not to you

Rob 

Here's a picture of a couple of cable ends, the wear takes place where the small end goes through the shift arm and makes for sloppy shifting. Eventually the wear is enough that the small shaft breaks right off if not checked

The wear takes place where the blue arrows are pointing, you pull out the cotter pin and pull the cable end from the hole in the lever to inspect it. These ends aren't worn, if they were worn you'd see a groove worn into the shaft.

One end or both ends is up to you.

https://ibb.co/PNWDbLz" rel="nofollow">

You may get by with one end but it's nice to check both

It's singing a chorus of "I've seen better days" 

https://ibb.co/3F33hr6" rel="nofollow">

 

My definition of slop is when you move the throttle handle and you don't get the same corresponding movement at the transmission end

So you move the throttle lever and with either barrel connector worn where it goes to it's corresponding lever, the amount of movement is less than the same situation with no wear.

An example might be.....you pull into the dock in Forward or Neutral and then hit Reverse, put it back in Neutral and turn the engine off. Next time you go to start it, you get nothing because the NSS isn't quite made up because of barrel slop

So before you try starting it again, you put it in Forward and back to Neutral and it'll then start.

Not an imaginary scenario, bought a boat with this issue and the connectors were both pretty worn and replacing both of them and adjusting the cable fixed it 

It might be one of those "you had to be there" situations

And Rob.........I bet me and TRB would agree your barrel end at the transmission looks good and if you put the throttle lever in Neutral and make sure the transmission lever is in the Neutral detent, then adjust the connector on the transmission end to slip right into the hole on the lever, you might be all set.

One thing you can do is test the switch while your cable is disconnected from the lever. Take a multimeter and hook one lead to one terminal and the other lead to the other terminal on the NSS and with it in the Neutral detent you should have continuity (roughly zero ohms resistance). Then move the lever by hand a little in each direction and you'll lose continuity.  (resistance will go to infinite or really, really high) It doesn't take much movement for the switch to open up. There's no need to remove the wires to do the test

So, test the switch, if it's good then do the barrel adjustment and see what happens.

Your second picture is a good shot of the throttle lever and it's cable end 

Up above it and hard to see is the shift lever and it's connector.

And if you want to bypass the switch, like you asked about in your first post, hook the two wires together on the same terminal but remember you can start the boat at full throttle in gear and hurt or kill people if you have a brain fart at the wrong time.

Ok fellas don't make fun of me - will this work to test NSS?

Google "multimeter" and you'll find a wide range of prices from a wide range of places.

You don't need anything fancy.

A trip to Harbor freight, Home Depot ,Lowe's, most any car parts place will find you a decent one for 30 to 40 bucks.

You can spend less and still get a decent one, or a whole lot more, but something in that range does everything you need for normal troubleshooting on AC and DC electrical systems in the boat, the car around the house etc.

Another free easy test of sorts would be to leave the cable disconnected with the local lever in the neutral detent and see if it cranks every time you try it or if it's kinda hit or miss. If it works every time, it's good