Your Tiger was an accordion model made for the firm Ernest Deffner in the 60's. The model was made by PanCordion of Italy and can be found with the name Tiger and also the Titano Badge.
The separation can be repaired. You will first need to pull the pins, remove the bellows, remove the reed blocks, and remove the grill. In the course of your repair
fortunately you will not have any celluliod issues as these Tigers were made with painted bodies and grills. I've repaired a few of these Tigers in the past and the following is the procedure I've used. --
First the materials --
(1) A 20 to 30 min. Epoxy such as -
https://www.amazon.com/Finish-cure-20min-epoxy-4-5oz-Smith/dp/B001NIC3VW
(2) A clamp with 6.in jaws that will open up to 12 in.
(3) A quantity of Isopropyl rubbing alcohol (to be used for removing excess epoxy before it cures).
(4) A proper length of bellows gasket to be used for replacement once the epoxy sets.
The procedure --
Remove the original bellows gasket. Mix the epoxy, force open the crack enough to accept the epoxy mix, apply the clamp and use the alcohol to remove the excess epoxy that is forced out of the separation ( the alcohol will not harm the painted finish)
Once the clamp is applied , set the treble section aside for 24 hrs. to let the epoxy to set completely.
Now as for the finish, as i've said earlier these Tigers came with painted bodies & grills and can be touched up with hobby paints.
I keep model paints in the shop such as --
https://www.testors.com/product-catalog/testors-brands/testors/enamel-paint/enamel-paint-sets/
and mix them for touch ups.
Let us know your results.