Yipes! You are into a complex and expensive area. For info, I have several pages on the fuel system parts, but I have them laid out poorly, so here's what I think you need:
Fuel Systems/Fuel System Illustrations/1985 & on F-Series
In the first link you'll see an illustration, towards the bottom, for 1985/87 F150/350 - 6 CYL. 300 (4.9L), 8 CYL. 302 (5.0L) & 351W (5.8L) UNDER 8500 GVW
- WITHOUT E.F.I. I think that's the right illustration - assuming you have dual tanks. And, if so, the part I think you worked on is 9189. Right?
If so, that's the fuel tank selector valve, as shown in the 2nd link. And, I'll bet the check valves were to ensure fuel is only returned to the tank from which you are running. So, w/o the check valves you may find that fuel returns to both tanks, and you could easily overflow one.
Gary, AKA "Gary fellow":
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Dad's: '81 F150 Ranger XLT 4x4: Down for restomod: Full-roller "stroked 351M" w/Trick Flow heads & intake, EEC-V SEFI/E4OD/3.50 gears w/Kevlar clutches
Blue: 2015 F150 Platinum 4x4 SuperCrew wearing Blue Jeans & sporting a 3.5L EB & Max Tow
Big Blue: 1985 F250HD 4x4: 460/ZF5/3.55's, D60 w/Ox locker & 10.25 Sterling/Trutrac, Blue Top & Borgeson, & EEC-V MAF/SEFI