how to test a distributor

Is there any way to test a distributor to see if it still works?

I saw the video. In your case, there is not much to test because it looks like the advance mechanism is all electronic. Imo install a new cap and rotor on the existing distributor. If the engine runs nicely, then you know its good

Its probably fine. The only issues that GA16DE distributors have is the occasional oil leak. The seal between the distributor and the cam/valve cover sometimes fails and fills the cap with oil.