I just checked #s you posted against parts diagram and confused again. I realize this isnt rocket science and should work, but thought I would post source of my confusion. According to pipe I have is like yours, but w.cooler photo shows a different looking pipe and part #.
What "cooler" are they referring to?
16572 HOSE, RADIATOR, OUTLET **571-61050 1 1980.08-1983.09 2F.. FJ40 $23.80 $17.60
Manufacture notes:RADIATOR SIDE
16572 HOSE, RADIATOR, OUTLET **571-61071 1 1980.08-1983.09 2F.. FJ40.. VKC.. USA $16.68 $12.34
Manufacture notes:RADIATOR SIDE,W/COOLER
16572 HOSE, RADIATOR, OUTLET **916-01056 1 1980.08-1983.09 2F.. FJ40 $15.19 $11.24
Manufacture notes:WATER PUMP SIDE
16572 HOSE, RADIATOR, OUTLET **916-01163 1 1980.08-1983.09 2F.. FJ40.. VKC.. USA $13.46 $9.95
Manufacture notes:WATER PUMP,SIDE,W/COOLER