Awareness (or feel) is critical to honing your golf skills. Whilst it can be informed and refined by extrinsic (external) feedback, it is at the very heart of motor learning. Feel is not a fixed trait, and can be developed and used to great effect.
Central to a human's motor learning abilities, is the continuous loop of information and instruction between brain and body. The brain perceives a task and sends messages to the body to prepare for action. Feedback sensors from the body send information back to the brain in real time, about how it's going. This allows subtle or significant alterations to movement.
The more aware we are of how we (or the club) is moving in space, the more scope for improvement there is. One of my favourite coaches, Fred Shoemaker compared video as a source of feedback to awareness saying:
Seeing your swing on video is the booby prize of learning
This is because you are seeing it after the event, and are not experiencing it. Real-time awareness allows real-time corrections.
Feel is one of five senses constantly transmitting information about ourselves and our environment. The problem can be competition, particularly from our vision.
So to drown out the sensory noise the simplest way is to close your eyes and your feel will be amplified.
Judgement off - be present
Inner monologues congratulating or berating ourselves whilst watching the ball fly are natural responses, but are in essence judgemental. While your brain is labelling whether something is good or bad, it is not free to simply observe.
This state where you are simply observing cause and effect, is sometimes described as being present. You are much more likely to make subtle distinctions about body or golf club if you are simply listening to your body.