What happens is of course is as you have suggested. The car is more than 30 years old, it is very likely to have all sorts of sludge in the bottom of the tank. The fuel pick up from the tank on these vehicles is attached to an arm on a float that sends the signal to the fuel gauge. This means it draws from close to the top of the fuel level of the tank. When you run it close to empty, the fuel is now being picked up from the bottom of the tank. Grains of grot/dirt/sludge tend to get sucked up and into the fuel system.
Ah, no. Sorry Dave, that bit is totally wrong. I do like and second the rest of your advice though! The fuel is always picked up from the bottom of the tank by a RIGID line with a sock on the end of it. There is no hose or pick-up point attached to the sender unit float (the float is purely for the fuel level sensing unit only). Whoever told you that the fuel was picked-up at the float was having a big lend of you.

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I would also exercise care when blowing a fuel line backwards. 1 - you might actually blow the blocked sock off the end of the fuel line, and 2 - if the tank vents are not quite clear, the pressure you just put into the fuel system with now push fuel back all over your face etc...

Start with the basics xale, cleaning from the tank forwards to ensure a previously cleaned part isn't blocked again.

Some (not all and I have no idea why I've only ever seen a few of them with it) of the ute/panel van tanks had a 7/8 drain plug in them from the factory, hopefully yours is one of these and you'll be able to drain the tank easily. Suggest doing this and getting rid of the crap fuel. The other option if your does not have the drain plug is jack the car (remember, high enough enough to actually get the tank out from under the car and please use stands!), drop the tank straps/fuel sender/fill and vent loop hoses (be very careful with the three-holed rubber grommet on the inside of the rear guard as they are almost impossible to get and a fair dinkum rego inspection will cause you to fail it if it isn't in situ) and drop the tank completely out of the car. You'll need a few containers and/or a decent deep tray to drop the fuel into. Flush it out, check for internal condition (use an LED torch here just in case you drop it into the tank while you're checking it over), check the condition of the fuel pickup/sock gauze (a lot of them have by now dropped off and are rolling around in the tank - it is better to have them fitted than left off), the vent and supply hoses and most importantly the filler hose and clamps - a good idea to source new ones now and replace the old ones as they will be perished from age, my HJ ute started leaking on me between Alice Springs and Erldunda one day and I wondered why it took me almost a full tank to get that 200km until I stopped and scoped it out. A dark country road (or in my case the outback) is not the place to have these issues raise their heads....

So replace what is neccessary or even looks sus and refit the tank to the car. That little job should take around 4 hours by yourself if you're not too quick with the tools, if you're handy or have good help it will take less of course. While you have the tank out, remove the fuel line from the fuel pump and (using compressed air) blow the fuel line forwards. If you have a filter fitted before the pump then remove it and blow it out to that point. Replace the filter and hoses as they could be part of the overall problem.

Fuel pump diaphragms do from time to time perish and the bits will either end-up getting stuck in the pump valves or being pushed-up into the carby. If you think it looks sus then change it. This means changing the whole pump these days as they are not a serviceable item like the originals.

Carby. The carby itself is something I wouldn't recommend you play with yourself unless you've had someone show you what you need to do as they have many little passages and fine metering adjustments that can make life hell if you don't get them just right. You mention that it is a WB - so should have a Quadrajet fitted? If it does, there should be a very small metal gauze filter in the inlet pipe union at the front of the carby - many mechanics/owners removed this gauze as they thought it would block up. Truth is that yes it did block up if there was rubbish getting through the fuel system, but the trade off is that if it is removed then the fuel bowl in the carby will be drawn back over night meaning that the car will be hard to start if left for a few days/weeks/months as the surface tension the gauze imparted on the fuel line stopped this drain back from occurring. If you can track down a carby kit, a can of carby cleaner and a couple of parts washing metal bowls, you're feeling confident and can swing a screwdriver with the best of them then there are many carby tutorials/information about with a decent google search. Things to watch are getting the needle and seat installed properly, making sure you set the float level correctly, make sure the accellerator pump plunger is correctly fitted and working and that all screws are nipped firm and not over tight. If your car has factory airconditioning there will be a small diameter return line to the tank. This rarely causes issues but you'll need to ensure this is clean.

There is no better way of learning your car inside and out than pulling it apart bit by bit and putting it back together yourself. You'll need to take your time, but you'll have the satisfaction of doing it yourself and save yourself some serious dollars. The flipside of this is that a carby is a specialised bit of gear to repair and if yours needs extra work (such as a distorted top plate on a quaddy or throttle bushes) it really should be done by a carby specialist as they will get it right.

Dave.