I went back and rewatched your video of the leak several times. Having watched it several times in a row, I do not think your issue is is at the pump/front of your engine. While both your pressure and suction lines run in that area, I think you have a hole in one of those 2 lines near the filter housing. Most likely culprit is one of the rubber hoses on the suction line, although it could be any number of things in that area.
Start by removing that off white side cover so you can see. I would closely examine the rubber hoses. As these appear to be molded hoses, if they are not available from hoye or fredricks, you may have to get creative with replumbing with straight pieces of hose.
Next closely examine the metal lines to see if they are rubbing anywhere. And may have a pin hole. Then check the filter housing and filter itself for damage.
One big caution, injected (in this case I believe transmission fluid (but any oil/gas/diesel based fluid)) petroleum product through your skin could be deadly.
View attachment 660305
This is from Hoyetractor.com. While the diagram focuses on the molded hose going toward the pump, it appears the same hose is used toward the reservoir. Personally, if I found a hole/split in one, I would replace both! Also I noticed while looking under mine (see photos in earlier comment) there is about a 3 piece of hose between the suction adapter mounted on the transmission and the metal suction tube going to the filter housing. My guess is that on both our machines, these pieces of hose are original and pushing hard on 40 years old.