So DNS's doesn't really work as Active/Standby.
Both GTM's need to be active, and the DNS client or the DNS Servers that look at your GTM's have both external IP's and if one goes down, or one slows down in its responce the other one gets used.
But what you do on the GTM side is synronise the configs between the two devices so they are always mirrored and up to date.
Hope this helps.
sorry by active standby what I meant is one DC is most preferred and other is least preferred. Now traffic from Local DNS what mechnism does it follow check the performance and forward the request.