I learned to play/sing this song and in so doing listened to it literally hundreds of times. Personally, I don't think any of the online lyrics get it exactly right. My version is below although if anyone has evidence I got something wrong or additional insight into the meaning of the lyrics, I'd love to hear it.

I'm pretty sure the song is about Gillian Welch's experience in the country music business. Although most country musicians were from Tennessee or somewhere in the south and grew up playing country music, Gillian grew up in California and didn't really start playing country music until she was finishing college at UC Santa Cruz. Verse 1 conveys the idea that she was seen by some industry insiders as a "pretender" who was not what she was "supposed to be", and a "traitor". As her Wikipedia page points out, her debut album Revival was criticized on these grounds.

The second verse suggests that being an outsider was a significant obstacle to her professional career. While insiders "caught the Katy" (a famous railroad line) and rose quickly to success, she was left with "a mule to ride" and her success took longer. Ultimately however "the fortune lady came along" and "walked beside", and Gillian managed to succeed in the business. The third verse ("every day is getting straighter") also conveys the idea that things got better over time.

After finishing her education, Gillian moved to Nashville to pursue a country music career but verse 4 suggests that living in Tennessee was frustrating and made her want to move back to California ("Leaving the valley...out of sight...go back to Cali"). By the way, I think "move the fader" is a reference to a mixing board in a recording studio.

Over time, of course, Gillian overcame all these obstacles, became a star, and was vindicated. Time revealed that she was not the "queen of fakes" or "an imitator" (outro), but that her music is authentic and powerful. Time's the revelator.

Here's my version of the lyrics:

    Darling remember, when you come to me
    I’m the pretender, and not what I’m supposed to be
    But who could know if I’m a traitor?
    Time’s the revelator

    They caught the Katy and left me a mule to ride
    The fortune lady came along, she walked beside
    But every word seemed to date her
    Time’s the revelator, the revelator

    Up in the morning, up and on the line
    Drivin’ to Corning and all the spindles wind
    And every day is gettin’ straighter
    Time’s the revelator, the revela—tor

    Leavin’ the valley, f***in’ out of sight
    I’ll go back to Cali where I can sleep out every night
    And watch the waves and move the fader
    Time’s the revelator, the revelator

    Queen of fakes, an imitator
    Time’s the revelator