Re: 1962 merc500
The only "tube" under the fuel pumps that i can "picture" is the one that goes to the bayonet connection, which you plug your external fuel tank into. There is the wireing harness which you connect your controller to.
There is also a tube which runs from the distibutor housing and connects just under the front cowl cover.
The engine will not run, or will not run properly if the stator is broken, however its a simple ohm's test to check if it is ok. If you have a Digital volt meter, you can easily test if it is ok. There should be a ristance reading between the two yellow wires. Make sure one at least is disconnected from the regulator. The reading varies between stators, and I don't know the correct value for yours. There should be infinate resistance between either of the wires, and the engine "block" or ground.
As for the fuel lines, if they are leaking or broken, they need to be replaced, I think you can buy ones for your engine. Otherwise you will need to buy fittings and fuel line hose, and connectors to make up your own.
The 1965 and prior sevice manual can be bought in book forum, or on a CD.
The Cd is avaliable on E-bay. I am not sure which book the site sells.
If the engine has sat for ten years, there is thread listed in the FAQ's (I think its in that section) about how to "wake an old outboard" you should read, before you try anything else to this motor.