WOW, talk about a blast from the past. Sounds just like my mom's old 76 Whirlpool. The sound of the sloshing during agitation made me think of the days when I'd sit out in the garage and watch ours wash. Congrats on the find there Toggle!
One thing I did notice in the video...when the washer goes into spin the tub on every Whirlpool I have had ramps up to the blistering 515 rpms rather fast. On this washer its not so. I cant help but wonder if something is going on with the basket drive clutch. It could be worn and its not an easy fix since the washer would have to be torn down to get to it.
My 3 cents
I noticed that the drain hose comes out at the top of the machine in the back and not the bottom. My 1976 Whirlpool LDA5800 has the drain coming out the bottom of the machine. Why is this? What year did the drain start coming out of the bottom?
So I tapped into the timer leads and she is well illuminated except during wash and rinse water fills (i.e. when the timer is stationery and unpowered).