Disconnected Vacuum Hoses

Good Afternoon Everyone,
I know vacuum situations are the most fun to deal with but I was hoping someone could help me out. I’m trying fix some mistakes and shortcuts the previous owner of my 302/5.0 EFI 1986 F150 made. There are several disconnected vacuum hoses I can’t find connecting points for, even after consulting the vacuum diagrams on the truck and on this website. I was wondering if some one could let me know where they run on their vehicle if they’re working on it in the coming days.
First is a black hose that originates at the back of the throttle body plate in two places then T’s into one hose just next to the distributor for me, then cuts overtop the engine and is hanging down by the power steering pump.

Second is on the left side of the engine and appears to connect to that junction box behind the battery. The open end in the picture is plugged with a bolt so I’d like to find where it needs to go. The end with the bolt in it is tan/skin color/light pink, then runs through a connector, where the hose/wire opposite of it is a bring pink and connected to the bottom end of the first terminal on the right in the junction box type thing in front of the battery.
I know that’s a lot but I’ll attach pictures. Any info will be helpful.
Thanks,
Nick

im not certain about all of your questions but I believe the one draped by the power steering is actually laying on the incorrect side. it originates at the throttle body and goes into a y fitting and at that time goes from two 3/16 hoses to a single 1/4 (approx) then "should" be run sweeping back under the throttle body and forward to the charcoal canister beside the battery. this will draw from the tanks to capture fuel vapors as part of the emission system.

Thank you, I was actually looking for the other hose for my charcoal canister so I guess that’s it.

Mat in Tenn has got that right.
I had a leak in my vacuum system right in that same spot.

The problem began when the charcoal canister broke loose and danced around until it had undone the hard vacuum line out of it on the way over to the 'Y'.

After untangling things, I was baffled why Ford decided to "Y" together those two vacuum lines off the throttle body so far away from the throttle body itself.  It adds apparent complexity to what should have been a very simple system to understand.

Actually ford did change that. Later models have a single 1/4” port on the opposite side with a purge valve and operates part time by the ecu