What exactly are you trying to clear? Are there screens that are gunked up?
If so, the easiest and a bit scary thing to do is remove the anti-siphon valve and/or elbow and using a stiff wire or metal snake, push hard until the screen tears open. Any pieces of screen if loose will just sit on the bottom of the tank.
If the check valve is the problem, you have two options in addition to cleaning it (don't bother). Replace the check (anti-siphon) valve or just use a straight through replacement fitting.
For the record, the ethanol is not the source of the gunk if there is gunk. Old shellacs in the tank get dissolved by the ethanol which in an ironic way, cleans the tank