Replacement Battery Help

Hi Guys,

I took the battery off my 2019 speed triple a few months to keep it on a optimiser. I'm now trying to put it back but got a couple of questions.

Attached to the terminals is an additional black box marked 30A, my questions is that on the back of it, seems to be a connector that would suggests it slots into somewhere on the bike, I can seem to find a logical place for it to slide into and don't remember pulling it out from anywhere when I disconnect the battery.

Second question is, I've watch other videos on removal and it looks like there's two rubber hoses (breather hoses) which connect to the take. I have one in place but not the second one, as you will see from the pictures which is this rubber hose for, should it be connected to the tank (it doesn't seem to stretch far enough and the end of it doesn't seem stretched enough like its ever been connected to the tank? Hope that makes sense, I've added some pictures to try and explain what I mean.


Cheers in advance