Switch/ electrical problem

I am a Newby to the 8n addiction and need a little guidance. I bought my first 1947 8n a few weeks ago. It has been converted to 12v and has front distributor. I had to replace the radiator, thermostat and hoses along with a new belt and battery. When I put the new battery in it would crank and run. It ran for about 15 minutes before it died on me- I think a fuel problem. That's beside the issue I want to raise right now.
A few days ago (AFTER I ran it 15 minutes before dying on me) I tried to work on it some and when I pushed the starter button the starter would rapidly click as if the battery was not charged. The key had been turned to the off position so I know that was not left on. I put my battery charger on and left it over night. Strange thing- the light on my charger shows "charged" but when I turn the key to the "run" position, in a few seconds the charger light goes back to the "charging" mode. If I push the start button it just clicks- with a one week old battery. The original manufacturer start button is NOT the start button. It's still installed but the PO rerouted and installed a push button under the instrument panel. Is there a way (or should I) cut the wires going to the swith(s) and hot wire the starter just to see if that stops the drain on the battery?[/i]

A first step would be to determine whether or not you have a 'battery drain'. You may not?

First off how old the battery is has no bearing on if it is good or bad. Over the years I have had many brand new batteries be bad right out the store door.
As for the starter just clicking that could be a bad battery or poor connections or a bad solenoid.
So you need to get the battery load tested to start with so you know it is in fact good then go from there.

One of the simplest and most versatile diagnostic tools you can own is a test light!

If you suspect a drain on the battery, be sure everything is turned off, disconnect one battery cable,
place the test light between the battery post and disconnected cable. If the lamp burns bright, there is a
major drain. Start disconnecting accessories until the lamp goes out. If the lamp glows dimly, there is a
minor drain. Try unplugging the alternator. If the drain goes away it is possible there is an alternator
problem, but a very dimly glowing light would take weeks to discharge a healthy battery.

Using the same test light, you can diagnose the no crank problem. You will want to "load test" the system,
that is to test when you are actually holding the starter button down. Start with the cables connected,
clean and tight. Place the test light leads directly on the battery posts, not the cables. Hit the starter
button. If the light goes out, very dim, either the battery is discharged or defective. If the light
remains bright, there is a problem with a cable connection, the solenoid, or the starter. Start moving the
test light, one lead at a time down stream toward the starter, testing under load until you find the point
where the lamp does not glow bright. Common problems are bad grounds and loose connections.