I will be interested in the answers that you get. I have an old WEN electric that has the same problem. The strange thing is that I can't even find the hole that the oil is supposed to come out. I wrote to them but never got an answer.

I am not sure how the oiler on Husky is set up. I assume it won't pump until the clutch engages. Did you throttle the saw when you ran it on your 30 second test?

The oil pump usually sits underneath the clutch. You might be able to see some sort of engagement mechanism. If you can pop the clutch (reverse threaded), you can turn that mechanism by hand. It might give you access to the tubing that the oil comes out of. You can check that the tube is clear. You may have a filter in the oil tank that you should check.

Take pictures as you go if you are not sure about reassembly. I always do in case I have any questions about putting it back together.

I usually check for oil by running the saw near full throttle with the nose a few inches over something (clear piece of wood, paper, etc.). The saw should throw a line of oil within 5 seconds. This shows that you are at least getting oil to the bar in somewhat sufficient quantities. The chain should definitely not be dry after doing this.