Sergey: 1) Where are you located in Washington State? In or near what city/town? Reason for asking is that there might be a forum member on one of the IDI forums living nearby who might be willing to offer some help.
2) I am surprised that no one bothered to mention WHAT the problem with your rear tank is. The problem is this: At the bottom of the steel fuel pick-up tube on the sending unit there is a Plastic CONE filter with a stainless steel screen. That cone sticks up from the bottom of the tank about 4 inches where it fits over the end of the steel pick up tube. That plastic one has broken off in is lying in the bottom of the tank, possibly in pieces.
The steel pick-up tube only goes down to about 3-1/2 to 4 inches from the bottom of the tank so when your fuel level gets down to that level the pick-up tube starts sucking air, even though there is 3-1/2 to 4 inches of fuel left in the tank. THAT EQUALS about 3-1/2 to 4-1/2 gallons of fuel that you cant pump to the engine because the cone filter is missing and the pick-up tube doesn't extend far enough down to reach that fuel. In effect you virtually are out of fuel. When you fill that tank up again it will only take 14-1/2 to 15 gallons, when the tank actually holds 19 gallons, which has been your experience.
This is a very common issue and it eventually happens to all of these IDI trucks and vans. Usually at about 20-30 years
It's
BEST to replace the entire sending unit
with a NEW one, including a new filter cone. (Why the whole unit?) There is a small printed circuit board in the sending unit, it's located in the white plastic part of the unit, near where the float lever mechanism attaches. You can see the edge of it in the photo below, you'll see an ARC that looks like a small protractor where the degree lines would be marked. Instead of degree lines, this circuit board has exposed copper 'fingers' along that arc. They are electrical contacts and I called them 'fingers' for visualization because if you stick your hand out and spread your fingers apart, your fingers would represent the contacts in that arc (except that there are a lot more contacts than you have fingers on one hand.) There is a contact strip, I think it is brass that moves along that arc as the float goes up and down, making contact with separate finger on that circuit board. Each of those contacts provides a different resistance value in circuit that goes to the fuel gauge. Each different resistance contact regulates the voltage to the gauge which controls the position of the needle in the fuel gauge, up or down.
NEXT: YOU MUST ORDER THE CORRECT FUEL SENDER, FRONT OR REAR FROM
YOUR YEAR OF TRUCK OR VAN BECAUSE Ford made several changes in the fuel gauge circuitry (resistance values) for diferent model years. If you don't get th correct sender for your truck or van model year,
the gauge will NOT work properly. BE SURE to order the CORRECT sending unit.
Here are links to the correct sending units for your rear and front tanks (respectively) and the filter cone. I HIGHLY RECOMMEND ORDERING BOTH UNITS for front and rear tanks because the front one will be failing soon enough and you won't know if the sending units that you need will be available when you need them. I waited 5 years before the correct on for my 1987 Rear Tank became available again. I just bought both of them about 6 weeks ago. I have not installed them yet.
Rear Tank SU:
http://www.trexautoparts.com/products/1985-1986-fordr-fs-pu-19-gal-diesel-rear-tank-su
Fuel Filter Cone:
http://www.trexautoparts.com/products/ford-diesel-in-tank-fuel-filter
Front (Side) Tank SU:
http://www.trexautoparts.com/products/ford-diesel-in-tank-fuel-filter
You will need a new filter cone for the Front (Side) Tank too.
For Full Size Ford Diesel Pickup Sending Units START HERE:
http://www.trexautoparts.com/categories/ford-full-size-pickup-diesel-sending-units
I don't see any sending units listed here for IDI Diesel Vans. I HAVE seen them listed online before. I suggest looking for a company named MTS. They also sell fuel senders for Ford IDI diesels. I don't have a url saved for that site and I can't search for it now. EBAY is another option.