[MENTION=78997]Drcoffee[/MENTION] is right, in the specific case of a 4Runner, there isn't any way that I could see the fuel pump unit (I'm talking about the whole plastic carrier that houses the sub-harness, fuel level float, the pump itself, etc.) to be the issue. On Corollas and other models there is a vapor line that goes through the fuel pump unit and we have had to replace them under a TSB or advisement from TAS for oddball refueling issues before; so I apologize for not clarifying that in my earlier post (was just generalizing causes in terms of likelihood for that concern).
That being said, that does still leave the Fuel Filler Neck, the Vent Line (including the filter), the Vent Solenoid, EVAP Canister, and the Fuel Tank Itself in order of likelihood.
Since you have an '03, the EVAP Canister is a "dumb" unit in terms of lacking the built in vacuum pump and self-checking systems the ones Toyota started using after about '05 do.
If you have an air compressor hand and you're not afraid of getting a little dirty, I'd try to locate the Vent Line that comes off the VSV for CCV (Vapor Switching Valve for Charcoal Canister Vent) and carefully unclip it from the canister and take the fuel filler cap off. The lines can be a bit stubborn and fragile so just take your time, maybe spray some washer fluid or water in a squirt bottle if it's caked in dirt. When you have the line off of the canister you can try puffing some compressed air into the line from the canister end so it pushes crud out through the open filler neck. It's not a guaranteed fix, but sometimes it can work; if the line seems to be really restricted or clogged you can try replacing the Fresh Air Filter (Part#77706-35010 should be the filter with the two lines). I have seen those fresh air filters get full of dust and debris and cause DTCs, EVAP issues, and refueling issues.
Here's the EVAP system components and routing from the FSM to give you an idea where and how it's routed:
If the fresh air line/filter seems to be clear and you get good airflow out of the filler neck I'd look at the vapor line from the canister to the tank (that should be fine as you're not getting any DTCs, but might as well look at it while you're there) and then also check the second vent/bypass line (smaller vapor line) that comes off the fuel tank and goes to the fuel filler neck. If all your lines are good, blow clear/not restricted, then you'll want to test the VSV for CCV to see that it is working. We can help you with that if you want, but if you're not comfortable doing electrical testing and/or don't have the equipment you can get a shop to test it for you.
Here's the EVAP system routing and location information to help you out.
