Pilot reported they taxied off the runway at night at FMN airport; striking a taxiway light.

Narrative

I had started the engines of the aircraft at XA:00 on the third leg of an all-night flight. In the twenty plus years I have been flying in the Southwest region; I had flown in and out of the FMN many times (50 plus estimated). When Taxiing out from the FBO ramp to Runway 07; the 'A' taxiway used to run parallel to the runway for the whole length of the runway. The taxiway used to cross Runway 05 right at taxiway 'A'. Apparently; as I found out after the incident; the airport re-located the taxiway to make a twenty degree turn when approaching Runway 05 and parallel 05 for a distance before crossing 05 further down. I did check for airport NOTAMs prior to the flight but there were none related to that taxiway as the project had been completed about a year ago. Unfortunately; I had not been into FMN in about two years so was unaware of the new taxi route to [Runway] 07.Additionally; I nearly always fly/taxi with our company iPad mounted with suction cups to the left window with the airport diagram open. This particular night though; the iPad had fallen off of the window into my lap on the previous leg landing in FMN. I was planning on remounting it after cleaning the suction cups and the window once back at base so on this leg I had left it sitting in my flight bag on the co-pilot seat. I was not overly concerned about the lack of an open iPad to refer to as I had flown into that airport so many times before that I felt I new the correct route. I was taxiing on 'A' slowly (I never taxi at faster than a brisk walk speed) when something ahead didn't look 'right' to me; I slowed a bit more and stared at the end of the runway puzzled as to why what I was seeing did not match my mental picture of how I remember that taxiway to look. In that 5-8 seconds of looking up at the end of the runway the airplane must have reached the bend in the taxiway where it becomes taxiway 'B'. I was rolling ahead slowly still on the direction of 'A' taxiway when the propeller hit the taxiway light. (I did not hear or feel a thing yet) and the airplane departed the taxiway and got stuck in the soft ground just on the side. Basically; the taxiway had turned but I did not. The propeller was damaged and is being replaced. This incident demonstrates what can happen when one's preconceived memory of things causes one to let one's guard down. Contributing factors were also not having the iPad open with the taxi diagram up. I should have at least checked the route prior to beginning movement. As one additional suggestion if this is possible with the FAA's new signage policies; a sign on the right side of the taxiway with and arrow depicting the bend in the taxiway with destination references of Runway 07; and 07 on it in Yellow with Black would be helpful to alert pilots. The time of the night and having been up all night at that point was also a minor factor I'm sure as it is human nature to not be quite as sharp mentally during those middle of the night hours. Also at that moment when something didn't look 'right' to me while taxiing; I should have stopped immediately. Slowing down a bit as I did was not enough.