I sound soo Texan in a recording - To myself I don’t.
I’m from a place in Ohio where people think there’s no distinctive accent,
But having lived elsewhere for 20 years, my ears perk up when I hear some of those vowels.
Among a group of my Indian relatives, my brother and I can drop into a drawl that the people around us have trouble understanding us, and that’s with an accent that’s supposedly fairly dull and indistinctive.
I can occasionally catch myself using pronunciations that are not native to my homeland, but it’s much more noticeable when it comes to vocabulary. For example, I habitually say “soda” now, instead of “pop,” although I always feel like a turncoat doing that.
Strangely enough, I grew up saying “sneakers,” even though it’s supposedly not native to that area.
I was born, raised and have always lived in Northern California. I am aware that I don’t have an accent. When I hear myself recorded that is confirmed.
I’ve always lived in and around Sydney (where I was born), and my family is Australian for generations back on both sides, yet for whatever reason, I don’t have a particularly Australian accent. I’ve been mistaken for being from pretty much every part of Britain, and I’ve even been asked if I was Russian. Yet sometimes, just sometimes, I’ll be speaking to somebody and I’ll hear a random word come out as an insanely caricatured old-time Steve Irwin style, fully nasal Aussie drawl. I don’t seem to be able to control it.
I have been known to code shift though - in remote towns and places, I’ll speak a little slower and a bit more Australianised, so that I don’t get beaten up for being a smug city arsehole. 
It’s impossible to speak without an accent.