That is the Touch-A-Matic 32, a single-line telephone, electrically equivalent to a 500 set.
Since it has no keys, it is not intended to work on a key telephone system. It will not work directly on a 1A2 system without modifications including conversion to A-lead control, and a line selector such as a 6040 key.
There are TAM-32 sets, equivalent to a x565HK set, that are equipped with a 5-line & Hold key that would work directly.
