That special musician also happened to be his father.
"My dad died of ALS, which is also called Lou Gehrig's disease, about five years ago," Gilmore explains via telephone from his Austin, Texas area home. "My dad and I had a real close relationship. Earlier in my life, there were times when it wasn't close."
"But in the early part of my life - my dad was a guitar player - we just deeply shared a love for this certain era of old time country music. The bond between us was really exemplified by this music. So this record was done as a tribute to my father and his musical influence on me."
When Gilmore refers to a "certain era of old time country music," he's actually describing a lot of great classic country tunes. This album includes signature songs by a few musical troubadours, such as "I'm Movin' On," popularized by Hank Snow, as well as Ernest Tubb's "Walking the Floor Over You."
One imagines it would have been tough for Gilmore to record this set of such personal songs.
"Actually it was the other way around," he explains. "It was a great joy for me. Of course, there would be moments when memories came up that were very strong feelings. But the nature of the way my father's personality was and the way our relationship was, there was more happiness associated with it."
"I had a hard time writing the liner notes. When you write about something that's close to you personally, you definitely can bring up a whole lot of feelings. So, of course, that happened. But in general, it was a very happy thing, and my only regret is that I really wish my dad could have heard the record."
Although Gilmore's dad did not get to hear this tribute, his father was nonetheless a big fan of his son's music while he was still alive.
"He was a dedicated fan, both of me and of The Flatlanders," Gilmore asserts.
And now, because his son often tours and plays with Gilmore, that country music appreciation is being passed down to yet another generation.
"My son was named for my father. His first name is Colin, but his middle name is Brian, which was my dad's name."
Artists often describe their recordings the way parents speak of children - meaning it's oftentimes difficult to choose any particular one over the others. And such is certainly true with Gilmore's relationship to his latest disc.
"Now I'm at the point where I listen to it maybe about every couple of weeks, and I've listened to it quite a few times since we've finished it," he relates. "And I've noticed that it kind of shifts from one to another. And every song on it I really love. That's why they're there."
Anyone who has followed Gilmore's career for any amount of time has probably already heard a few of this album's songs in concert. So it's not as if he's gone back and dusted off a few favorites.
"These are songs that, for the most part - with a couple exceptions - that I've done all the way back to when I was first learning how to play, that I sat around with my dad and sang them with him."
When Gilmore's dad passed down his love for country music, he did so quite naturally. "It wasn't, like, in any kind of calculated way," Gilmore clarifies. "My dad had such an intense love for it himself, that it either rubbed off on me, or I got it through his genetic makeup or something."
No doubt, many listeners will be immediately attracted to Gilmore's near-definitive version of "Saginaw Michigan" here. Not that there's anything wrong with Lefty Frizzell's original, but Gilmore just puts so much angry emphasis into its words, that he sells the song to complete perfection.
"That song is a really fun song to play live," Gilmore enthuses. "My approach to songs is to really get to the song and the meaning of it and to really convey the lyrics and the feeling of it. And in that song, it's such a funny tongue-in-cheek thing. A lot of people kind of get it - get the joke of it - for the first time when I'm singing it. I really enjoy that. A lot of people that really loved the Lefty Frizzell version, it was more like they were just listening to his voice and not really paying much attention to the lyrics or the story."
At this writing, Gilmore hasn't really toured a whole lot in support of this new album.
"When I tour, sometimes I play solo. But lots of times I play just a duet with me and Rob Gjersoe, who's the guitar player that's all over this record," he says. "And you know, on a lot of these songs, Rob will be playing three of the instruments. If I have a full band, I'll do all of these songs off of this record. If I'm just doing it solo...some of these songs are just so band-oriented, that you can't really do it justice with just kind of a folk-y treatment - solo guitar or duet. It's dance music."