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Wait, are you the kind of people who regard the nomadic people were just similar to each other?
In Chinese information websites, the Gokturks were believed to value investigate and scouting. According the record of Tang Dynasty, the Gokturk army used “Komg” a lots, who are the scout troops and regarded an important part of their warfare. For example, in 630, the Tang army “surprisingly” bumped into about thousands Gokturk scout camps at Yin Mountains. Later, Emperor Xuanzong was warned by Gentleman Attendant at the Palace Gate (黃門侍郎) Zhang Tinggui (張廷珪) that the enemy uses scouts so there must be prevention. You can check 李靖傳事狀 and New Book of Tang, volume 118 for what I stated above.
Cavalry archers were indeed the forte of the Gokurks, which was also said by Emperor Taizong. However, the Gokturk infantry also cooperated with their horsemen well at rapid aggressions. In their system, one-third were infantry and two-thirds were cavalry. For example, Kul Tigin was a prince and a general who achieved brilliant results by leading infantry fight. This means that the way the Gokturks fought did not always focus on the nomadic stereotypes of hasty raids and irregular offensives, even if they were actually good at these things too. They may place more emphasis on the formations than people think.
So they may have a hunting bonus, full champions, free heavy cavalry archer upgrade and a bonus or cheap UT to greatly increases unit’s LoS. Their heavy cavalry UU may be named “Fuli” or “bori”, mean “wolf”, who were imperial guard corps of the ruler, able to keep moving, attacking and sustaining damage for 3 seconds after HP down to zero.
After studying the relevant details and literatures, you will find the clear difference, create a different civ and no longer think they fit each other such well, otherwise we have not needed to introduce any new civ since AoFK.