Or maybe, even though not capable of rusting, the aux tank is certainly capable of gunking up over the years. Especially if the previous owners (or are you the PO?) never ran the aux tank.
I know back then it wasn't unusual for someone to keep the "spare" tank full, but almost never use it. Keeping it strictly for reserve duties.
Or with today's modern fuels, you would not have to do that for very long for some buildup to happen.
Does it go away immediately as soon as you switch back to the main tank? Or do you have to go through other motions to get it running correctly again?
OR, another or... Maybe that same sock filter that Oldtimer mentioned is simply deteriorated to the point that bits and pieces of it are being delivered to the carburetor along with the fuel.
At this point, if it's anything like that, then you're pretty lucky that it goes away when you switch back to the main tank.
Personally, I would normally just run the aux tank dry and then remove and clean it. But in your case since it's way too consistently puking fuel on your engine, I would drain it by other means and then remove it. Check for deterioration of the sending unit and fuel filter. Visually inspect it for a film on the interior and clean it if possible.
And even then I would probably put an additive in the gas at the next fill up (both tanks maybe!) and use it to dissolve the last bits and maybe even clean the carburetor.
But you may end up having to pop the top off the carburetor anyway, just to clean out anything left in the bowl.
It should not normally in practive be something like one tank building up pressure and then push it through the pump to the carb, but you can verify/guarantee it's not the issue by simply removing the gas cap before the next time you try using the aux tank.
If you feel a rush of air come out, or if the problem goes away, that might have been at least part of it.
But gunk sticking the needle off the seat in the float bowl would act just like over-pressurizing the system. Gas will get paste the needle-n-seat either way.
What would be surprising is if it goes away as soon as you switch back to the main tank. Usually gunk remains until you clear it, or drive it enough to clear it.
If it's pressure however, that would certainly clear up as soon as you switched tanks.
Good luck.
Paul