Interesting question - being a free-diver myself this is one that I had to master to gain the ability to go beyond the conditioned reflex to dive deep into the sea for more than 3 minutes at a stretch - battling my bodies own gag reflext to gasp for air.
Firstly understand that this is something that only comes through intense training and mastery over the mindbody.
The gag reflex associated with something that disgusts the senses and the one that forces you to gasp for air I guess would be the two main hurdles to work towards training.
For both, mentally you will only be able to "suppress" or hold it back for only a short time. The key is to train both mental and physical aspects of your self to control the mechanics of the reflex.
For something that disgusts the senses being mindful of your inner dimension will be your best companion, returning to an awareness of your own deep rhythmic breathing, sensations on your skin, etc. to essentially take your mind off of what is transpiring before you - with time the gag reflex will take longer to arise until it just isn't that bad anymore.
For the instinctual reflex to save your life it will take practice and determination, knowing your limits and pushing closer and closer to them in methodical practice. It took me for example 6 months of training to hold my breath for 3 minutes while diving underwater to 20 meters - free-divers dedicate their lives to break the 5 minute mark, some even losing their own life in the process.
In this case meditation is imperative both to slow down the heart rate and to establish control over the mind-body connection. The more connected you are to the sensations within your body and the signals being sent from the brain, the more attuned you are to controlling them.
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