Broken lube lines should be noticable, extra oil in coolant, or puddles on the floor.
Many systems with broken lines will still seem work properly because the switch will momentarily operate at the start of the lube cycle.
So the real question is does the switch work (doing it's job) and the pump is not pumping oil?
Manually operating the pump means that it can pump oil,
but there are several things than keep the motor from operating the pump.
1. Worn out clock motor, runs but does not turn the output shaft.
2. Some other worn out component between the motor and pump.
So leave the switch out of the threaded port and run the pump for a half hour or so,
or until more than a small drizzle of oil comes out.
My vote is it's a pump issue and the switch is doing it's job, keeping you from running with no lube.
In my experience, it is 10-20 times the pump and only once a switch, and when the complaint is oil in coolant or on the floor, it is a broken line.
Many times the owner screws a switch into a port with the wrong thread (NPT vs BSPT) and causes more problems to fix later.
Just my 2 cents,
Bill