Not sure these are the sort of strange you're asking for but here goes!
Hendrix and Beck were inspired after a visit to the Yeoville Fleet Air Arm museum when I went on holiday across the country for a bit a few years ago. I picked up a lot there that stayed on my brain and wanted to do something with it. The thing that made the characters stick was an exhibition showing some of the letters sent home (some of them were very sad and harrowing). I couldn't find enough on the Falklands (what the museum mainly focused on) to feel comfortable writing something in that setting so I briefly had these two set on a sci-fi aircraft carrier after watching a documentary on HMS Ark Royal somehow got me thinking about how an aircraft carrier in space would work before deciding they worked better as historical characters and settling on WW2 for their setting.
Francis happened when I still somehow managed to be seasick after taking anti-seasickness tablets (and I'd given them enough time to kick in) on a small ship I help crew on leave. I was pretty embarrassed and felt awful for it. The mental image of an Age of Sail captain being seasick popped up and I hung onto it because the irony amused me and made me feel better. It distracted me enough for the seasickness to ease off a bit I was eventually able to go back on deck and help with the mooring lines as we came back into the harbor. I developed the mental image enough that I did something with it once I'd slept it off at home! Technically Owen started to develop around the same time because I am incapable of having 1 character in a setting they've gotta be in pairs at least because I enjoy developing character dynamics as much as I enjoy developing characters but it was a few months before I solidified the mental image of him enough to try drawing him.