How to get to Gyrospire Beza & Zeka
In order to reach Gyrospire Beza and Zeka you will first need to go to Fortress Mechanotus. The fastest way for you to reach Fort Mechanotus is by taking the Guild Hall to Dragonscale Hills and then traveling northeast from where you zone in to the large machine that catapults you up to Fort Mech.
Once you're in Fort Mech you'll find the zone line for both Gyrospire Beza and Zeka just a tad bit southwest from the location you zoned in. There will be two smaller catapults by the edge of the cliff - one of them is for Zeka and the other Beza. Click on the one corresponding to the zone you want to go to and that's it!