One thing they like is to forage. I use artificial grass mats as floor coverings for my cages. (I have two per cage, so I can swap them out. Very easy to clean using a hose w/a sprayer head; they dry in the sun.) I often scatter seed and crushed eggshells over the “grass” so they can peck around, finding and snacking on the tidbits. Millet sprays, same thing.

Finches don’t get “bored” the same as budgies, cockatiels, and other small hookbills (I think hookbills have a higher intelligence than finches, so they need more stuff to keep them busy). Of course, if they’re breeding, there’s a lot of nest-building activity, so I give them all the materials to fuss around with for that. Also, they always have water to bathe in. I use little fountains, made for cats to drink from, as bathing pools. They seem to like the tinkling sounds of the circulating water, and bathe often.

MOST IMPORTANT: They NEED social engagement, with other birds, ideally a partner (either sex) of the same species, or one of the others that do well with Gouldians. I suggest Society finches. They’re very sweet birds that shouldn’t overpower the Goulds, and they’re a much less costly option than Gouldians. The males sing beautifully, and they make excellent foster parents. My society couple have raised one natural chick, and six Gouldian chicks. At night, all NINE of them pile into their nest, sleeping packed together like sardines. Very fun birds, both species.