If you leave it on prime all day while at work, there should be a puddle under the bike at night when you are ready to go home.
As a vacumn assisted system, fuel will stay in the tank when the petcock is on run, or reserve as long as the bike is not rumming. However, in prime you are relying on gravity alone and gravity doesn't take the day off while you work and doesn't care if the engine is running or not..
The " choke" is an enrichener, and as such doesn't reduce the air portion of the air/fuel mixture (as a choke would) but rather puts more fuel into the mixture. This is why when you pull out the enrichener, you should not turn your throttle when starting it. That will flood the system.
Battery sounds suspect, fuel lines are old enough to need replacement.
Have fun and let us know how the beater search goes.