I usually don't feel the glutes firing when I'm seated unless I'm in a really long and hard climb or if I stand up and move back.
Is there any common adjustment to maximize the glutes utilization? Or a common mistake?
Cyclists often become quad dominant in their movement patterns, where the quads are preferred over other muscle groups, such as glutes, for a task where both can be involved. This can start to weaken and de-conditioning of glute muscles, causing the body to further prefer quad dominate movement patterns (i.e., reinforcement). A quick test can be to do a squat and then stand, if you find yourself driving from the balls of your feet rather than evenly through your heels and balls of your feet, you are likely favoring your quads over your glutes (or you could have a short torso and long femurs - no test is perfect).
If you have become quad dominant simply changing your position may not be enough to get your glutes firing effectively as you may have: A) de-conditioned the muscle; B) trained your neural pathways to de-emphasize glute recruitment in favour of quad recruitment; and C) if this pattern has gone long enough lost flexibility which could further inhibit movement patterns emphasizing glutes. As such may also find the glutes only fire when working very hard because the nerve impulse is finally strong enough to get the muscle to contact effectively.
Assuming you can fire your glutes well, a saddle position where you can roll your hips forward slightly allows the glutes to be recruited easier through the bottom of the pedal stroke. Saddles with a swoop profile (i.e., high tail) facilities this position. I also personally find if I focus on supporting my upper body weight from the front of the hip this seems to further encourage the glutes to engage (rather than rolling your mid to lower back which rolls the top of hips backwards). To set up these types of saddles, set a level on the middle third of the saddle and adjust until horizontal, this should be a good starting place, overall the saddle will appear somewhat angled down, but this is a visual trick caused by the swooping profile. Some may find this type of position difficult if they lack mobility in their thoracic region of the back or core strength (e.g., constant slouching posture can lead to a reduce thoracic range of motion making this type of position difficult).
If you are still having trouble, you may also need to strengthen your glutes and train your ability to fire them. Squats, bridges, lunges are some basic exercises that can help, but they require good movement patterns to fire the correct muscles, for example you can compensate in a bridge by recruiting your hamstrings instead of your glutes. As such, it can help to get a trainer to make sure you are doing the exercises properly, otherwise you may simply reinforce compensatory movement patterns in order to get the “task” done.
Finally, improving glute strength will also help reduce repetitive stress injuries as they also are important component of hip stabilization (e.g., gluteus medius are often weak in cyclists - the link has a good exercise for this). In terms of power, I found getting my glutes to fire properly again after years of poor posture was worth about a 20-30 watt advantage on my FTP.
This passage from "Bike Fit" by Phil Burt (lead physiotherapist for British Cycling and a consultant physio for Team Sky) describes pelvis position and the impact of thoracic mobility.
Posture is the maintenance of a certain body position and requires appropriate joint mobility, joint/muscle coordination and muscular endurance. Limits in any of these elements can result in postural irregularities. Good posture on the bike required good flexibility through the hamstrings and the glutei muscles: this allows the pelvis to roll forward, keeping the back in a straight position while reaching the handlebars.
One major factor limiting the back's ability to remain relatively straight while on a bicycle is thoracic immobility: lack of movement in the middle of the spine normally results in the spine flexing too much. Excessive spinal flexion while on a bicycle will limit breathing and compromise your ability to stability your spine for torque production to the pedals