I think the oil pumps are incredibly simple in design and are the way to go, assuming your tank is in good condition. To test mine (I’ve done 3), I put premix in the tank, then disconnected the line from the pump to the carb or intake at those places, depending on the model. The line should be empty and clear (to see through). I just replaced the line that was there to make this work. It probably needs replacing anyway. Then start the engine, running premix (I did 40:1 with semisynthetic oil in the premix, because that’s what I use in other equipment). Then look for oil flow going through the line from the pump to the carb or intake. It’s very slow at idle, but if you’re running premix, it’ll be fine to rev it and look for oil going through that line. Once you confirm oil is going through the line and is dripping out, connect it to the carb or intake (depending on the model), drain the rest of the premix (or not, it won’t hurt it for a bit), refill with straight gasoline. Non ethanol gas, preferably. Ride and enjoy!
People say they can fail, but anything on a 40 year old bike can fail. If the pump is in good condition, and not rusted or clogged, it should continue to function well. There’s a YouTube video on how to clean it and get it apart. Try searching for it. Could replace the gasket where it seats into the casing.
Or as little evil suggests, refer to the manual.