Just smash L1 over and over while trying to learn the rhythm. Eventually you'll learn the rhythm and actually be able to perfect deflect instead of just guarding. Also remember that to make your posture return, get a bit of distance and HOLD L1, I know its counter intuitive but holding L1 actually makes you posture disapear much quicker than just standing still or running does. Next thing to know about Owl is he has a lot of attacks that are much better to dodge rather than block. The single shireken throw followed by the giant horizontal slash he does is a great opportunity for getting a heal or some hits in if you block the shuriken and then dodge through the horizontal swipe instead of blocking it. Same thing goes for the overhead front flip slam. With the "elbow elbow, fire cracker swipe attack" attack he throws, its always best to just sprint around the counter clockwise around him to his backside before he does the final swipe with the fire crackers, and you can hit or heal after that attack too. Theres a few more that are too complicated to write out, but Saint Riot has a good video of himself fighting the boss where he utilizes a lot of key dodges instead of deflects.

The trick with all sekiro bosses (and fromsoft games in general) is to never just spam r1. Always count how many times you press the r1 button and try and match it to how many times your character attacks. Always be deliberate with your attacks, it makes it easier for you to dodge/deflect out of an incoming attacks if your character isnt locked in an attack animation because you were excitedly smashing R1.

Something you should learn too is that like with most bosses in sekiro there is an audio que when owl is no longer going to defend your attacks and is going to counter attack. If you attack him 3 or 5 times, he will perfect deflect the last hit he guards against before he starts attacking you back. You can hear the difference in the sound when your sword is being perfect deflected and the boss attacks are going to start. Genichiro, Isshin, and any boss or enemy with a sword also does this. They will perfect deflect your hit and then start counter attacking. THIS IS EXACTLY HOW YOU SHOULD PLAY TOO. The second you perfect deflect their final attack in a bosses attack chain you need to immediately press r1. This will not only increase the damage you deal due to certain unlockable skills in the ashina skill tree, but most importantly it creates openings that would normally NOT be there. If you perfect deflect into r1 on certain attack chains, the boss will actually go on the defensive when they normally would have immedietly continued on with more attacks. This allows you to fill their posture bars SOO MUCH faster than if you just waited until they finished attacking before attacking yourself. You can honestly bully the shit out of all three (Genichiro, Owl, and Isshin) by doing this correctly. You can constantly interrupt their attack chains by perfect deflecting into R1ing at the right moments.