"...It is still an individual approach and response that depends entirely on the capacity of your body and spirit..."

Something that is closely related to mountaineering, and is not a part of the basis or with clearly prescribed rules of movement, technique, and instructions for proper use of equipment, is the factor of how we, ie our body, handles the very act of mountaineering manifested through proper pace, breathing and rest.

There are several guidelines and recommendations on how to properly breathe when mountaineering, when and how much to rest, what pace to apply, etc. but my opinion is that it is still an individual approach and response that depends entirely on the capacity of your body and spirit. 

In this context, I would also add that you may be able to consciously influence your breathing or pace, but it could be more difficult to influence, for example, the work of your heart or the speed of oxygen exchange in your muscles. That is why I think and recommend that everyone should find and adjust to what suits them best with small deviations if it is a group movement or a specific terrain. 

Any excessive and unnecessary forcing of the body can lead to catastrophic consequences for your health and life. Here are short explanations and recommendations for people with normal fitness and readiness:

Pace

The pace can be manifested as the speed of your movement through mountainous terrain. The pace is a combination of 

• the readiness of your body - fitness, characteristics of the path (uphill, downhill, crossing rocks or rivers, etc.) 

• weather conditions from the day in question (sun, rain, wind, temperature, humidity) 

• the time of year

• how much load you carry on your back (backpack)

• whether you are alone or in a group

• group composition (children, adults) 

• many other smaller factors.

My experience says that the pace should be adjusted as required by all the above conditions by taking into account that it is most optimal to move evenly, and thus the strain on your body will be even. In general, when it is uphill, I recommend taking shorter steps, to move at a reduced speed, preferably in a zig-zag trajectory on the ascent path, and thus the load on the heart and blood vessels will be reduced. The same goes for moving on steep terrain and thus the body will practically not be exposed to high loads and the risk of injury and problems will be lower.

It is generally recommended that the heart rate is within 80 to 140 beats per minute, depending on the age of the climber. So with this rhythm, the speed of movement - the pace will be dictated by your heart. Here it should also be noted that there are mountaineers who practice fast pace and I recommend that they always leave an atom of energy in their bodies, as if after the tour is over they still have the strength and power to continue for some time.

If you move in a group, then it is desirable to adjust the pace to the oldest member of the group, or possibly if there is a child in the group, then you should move according to the pace of the child.

Breathing

Breathing is closely related to the work of the heart and depends on several factors such as pace, terrain that you mountaineer on (uphill, downhill, plain), altitude, length of the path, and others. Breathing while mountaineering is almost always more intense than normal resting breathing. It is recommended to breathe evenly on the nose, without talking, because talking negatively affects the rhythm of movement and thus the work of the heart and overall motor skills. 

However, with increasing effort, through faster movement, increased load on your back, the slope of the ground, higher outside altitude, a lower percentage of oxygen in the air, there is an increase in the rhythm of the number of inhalations and exhalations and thus nasal and mouth breathing begins or just intense mouth breathing. 

In this case, it is necessary to take a break or significantly reduce the pace as needed to regulate breathing and then resume mountaineering. It is often recommended that the number of inhalations and exhalations be harmonized with the number of steps, but in reality, this is very difficult. It is feasible and advisable only at constant loads for a long period and then it is harmonized according to the principle of one step - an equal number of inhalations and exhalations.

Rest

Mountaineering rests are always in function of safe mountaineering and as such are often individual things and need. Rests should always be in a safe place on the mountaineering route and should regulate the effort your body is exposed to while mountaineering. This means that resting irregularities in breathing, caused by accelerated or uneven pace, should be regulated, ie the body should be calmed down, the muscles should be relaxed. Mountaineering rests should be moderate (from 1 min to 3 min) and more frequent (at intervals of 20 min and plus) depending on the complexity of the terrain that is mastered and other factors. These rests should be used for physiological needs, consuming fluids, fruits, and small energy meals that will make up for some of the lost fluids, salts, and minerals. 

During these rests, one should pay attention to their timing, because if the time is exceeded, the opposite effect can occur, which will negatively affect the further ascent, such as cooling the body, relaxing the muscles, etc. After a few hours of mountaineering, it is possible to take a longer vacation that would again be in function of the above.