You have the original (old-style) Ross system.... They can be a bit cantankerous at times.
Without digging thru my TM's, if memory serves me right there is no filter on these units other than the fill screen, as you saw... But I do remember the LO's on these trucks with the old-style Ross boxes require SAE10W motor oil in the steering reservoir, and also SAE10W in the steering box... 8-1/2 quarts in reservoir , 2-1/2 quarts in gearbox if I recall correctly. I believe a free download of the M39-series LO is still available via SB member jatonka35s.com website. (and it's also available right here on SB in the TM section tab, under 5-ton)
If the old-style PS gearpump shaft seal is going bad, you would lose fluid and not see any leak. Your engine oil level might go up, depending if engine burns or leaks oil... If yours has PS fluid or ATF in it, the fluid might be too thin for the pump shaft seal to hold it, and also too thin to keep adequate pressure when warmed up (especially in an old pump) for the steering to work well.
Of course you could also be having a problem with the diverter vane (or whatever it's called) inside the PS unit on the gearbox. But usually when that's failing you are able to steer one way okay, but in the other direction it steers really hard. Thus, it sounds like that vane is not your trouble.
Your steering hesitating and then going again is a symptom of low oil level, among other things. Re-check your fluid level.
Eliminate the simple things first. Also, I would drain whatever is in that reservoir and also drain what's in the steering gearbox. Refill with SAE10W. Since you're in Texas and perhaps the PS pump is worn, you might think about trying SAE20W, if you can find it. Anything you want to try with steering is at your own risk, I'm not assuming any liabilty here.
I have old farm tractor hyd systems calling for 20W summer, 10W winter. These old hyd systems were built for motor oil and therefore should remain so. I hope your problem is the simple one.