Good idea to apply power directly to fans to see they are operational
Another (informal) fan test: spin the fans by hand to see if there is resistence...if the fans have resistence it is mostl likely from dirt/muck accumulation & the bearings may be toast= aux fan replacement(s) may be necessary
it is common for dirt/muck accumulation over the years to affect fan performance and eventually cause their demise
I've seen the aux fan wiring harness also melt due to the heat generated from this type of condition- - fix for this condition is to replace failed aux fan(s) or their bearings, wiring harness, fuse(s)
I agree with you that things are pretty tight around this area.
hope this helps and best regards