This is not a joke, my hose blew while on a roadtrip and somebody took that picture, now that this has been fixed. I circled in red a hose coming from the back of the head, to a black module of some kind, with another coolant hose going from that module, into the firewall.
I'm guessing this is the heater control bypass?, what is the Toyota part number for that? and where can I find this in the TSRM.
also, is it common for that piece to leak? everything started to leak and blow(hoses) after I switched from a leaking radiator (couldn't hold pressure) to a 1.1 bar Mishimoto.