I think that is the EBCM (electronic braking control module), I may be wrong though.

Ya William, what ever box is, it is going to be hung up & away for when this job gets done.
I ended up ordering the larger diameter hose 25mm form GM (1 week away) but the smaller Diameter hose is simply (so far) not available here and GM disco'd it.
Rock Auto is good for hard to find parts and generally has em in stock.
I put some electrical tape tight around the cracked hose area, and then a bit of duct tape followed by a pressure bandage consisting of some 3/4 inch hose & ring clamp.
That should hold it for a while until I can get the correct hose here...LOL.
Oh and the price of those spring clamps new are like $12 each, ring clamps please!

Last night I followed William'* suggestion and used the tool he mentioned on Amazon. It still took a great deal of time and frustration, but I was able to get the hose clamps off enough to get a razor knife on the ends and pry the hoses loose. They were fused to the fittings. I would never have been able to get a regular set of pliers in there to do the job. I did use some spray silicone on the hose so the clamp slid back fairly easily. Otherwise it would bind and not move. Hope that helps when the time comes! I'm sure glad I won't have to deal with spring clamps again. I will soon use the tool to remove all of the clamps and be done with them! Good Luck!!

Happy to hear the tool was helpful, and that you were able to replace yours, nice job!

UPDATE:
Finally I have both heater hoses. Have had the larger GM one for a few weeks but have been waiting for the smaller diameter 5/8 (that GM discontinued) to get in from Napa as was back ordered by the maker Gates. I guess they got around to producing it and can show them together today !!

Will work this weekend to install both and use ring clamps.
I am also overdue for a synthetic oil change, just got a tall 1036 Napa Gold filter too.
Will be a relief with the hot weather here, not to worry about these hoses splitting from age.

Nice, new parts excite me almost as much as toys did when I was a kid during the holidays, or birthdays even.

Let us know how it goes, I hope it is goes smoothly for you!

Art put your patience cap on! Good luck...

Allowed PA to cool for 2 hours then using the correct KD tool, It was no problem to remove the GM clamps.

The smaller diameter hose had the beginning of a split and I decided after careful inspection of the other larger diameter heater hose, that only the one hose needed replacement. The Gates hose from Napa was a perfect fit,no trimming required at all.

After using the KD tool it was discovered that the GM clamps were in perfect shape and perfectly round, so they were easily re-used with out any leaks. These clamps I like better personally.
It should be noted that no draining of the rad was required. A small pan was put below car and I drained only a few cups of coolant into pan. I disconnected the first clamp and pointed the one side of disconnected hose down towards pan, allowing to drain, before removing the other clamp and then the entire hose.
The rad cap was left sealed during the above.--DONE--

Always feels good to have new parts on your car. For future reference i've had good luck with channel locks/adjustable pliers to get those hose clamps off. If you have enough room that is. Of course it is another excuse to add a new tool to the tool box lol.

Very nicely done Art!
Glad the job was not too bad for ya, I still do not look forward to whenever I do mine!