It seems like your job at the museum you are being paid to be available and to respond when needed during certain hours. If it was an IT job, it would be the equivalent of being "on call."
Your software development gig is being paid by hours worked and work product developed.
As long as there are no formal prohibitions, I think you are okay, if in somewhat unorthodox territory here, provided -
If you are deep into some complicated or intensive coding, and any kind of alarm or other event happens that you are expected to respond to, you go above and beyond and respond immediately, even if you feel it's not needed to be exactly right away. You don't even want to see where the line between ethical and not is, since you are essentially getting paid by two employers for the same work time. Again, you are being paid to be available to respond, and to respond as needed, so that is your #1 priority, over all other considerations. If you wait a few minutes to wrap up the coding, then you are, indeed, not fulfilling your obligation to be available to respond.
If you are doing software development work at the museum from 8 PM to 2 AM, and alarms go off and you need to attend to it, and deal with police, etc, for an hour, you better not bill for that hour on the software side. They should only get billed for five hours, or less if you took some breaks. Even though, potentially, they would have paid you for all that time developing, you didn't actually spend it all doing the work, so make sure you don't bill them if one job's responsibilities don't allow you to actively engage in the others'.
The only other consideration is if you're making use of a lot of museum resources while computing - if you're using a work machine to connect to the Internet and working like that, which it appears you are not doing, that would not be ethical. Likewise, if your work means you are using Internet connection and data throughput via the museum's physical network, that is also potentially problematic. Hopefully your development is all done locally, network-wise, on your laptop. If not, since you are getting pretty much getting double-paid, it's not too much to ask to invest in a data hotspot out of your own pocket.
If you have all of that covered, ethically, there shouldn't be an issue about talking about it in an interview. First of all, if I see a resume where someone has "independent contractor software developer," along with something like "night shift security at the museum," I'm not going to assume that both were during overlapping hours. In fact, I'd assume one was a "second" job. Just like if I saw "CFO for GE" and "Bartender at the West Side Businessmen's Club," I'd assume they didn't occur at the same time.
If that's the assumption, it probably won't come up, and they're going to assume the museum gig supplements the developer job.
Also, if sitting in a chair and waiting for an alarm to go off that never goes off has no relevance to your next developer position, I probably wouldn't include it on my resume, even if it was a night shift vs day shift situation, because it does not add any value to my resume. Just like a CFO from GE probably wouldn't bother listing his bartending gig if he was after a CEO job for his next opportunity.
Now, because you're asking, and it's on your mind, it may seem to you like you're hiding something, but, really, if you asked "should I include my night job at the museum on my software developer CV/resume" and the hours did not overlap, I think the advice would be "no." So leave it off, and it should never come up.
Now, if, as an independent contractor, they need some kind of supervisory reference, then I'd bring up that I worked as a warm-body to watch for alarms going off after-hours at the museum as a second job, but then, in that case, again, the hours overlapping should never come up.
Again, I don't think this is deceitful, and volunteering it when it isn't even on the radar not only puts it there, but raises questions, in their mind. "I didn't care, so why is he so eager to put my mind at ease? What's REALLY going on here?"
In a job I had, there was an ongoing system overhaul of the core IT system. I heard about it, in was called "Next Gen" as a project. In my first all staff meeting, the director in charge stands up for their project update and says, emphatically "First of all, EVERYTHING IS FINE!"
What did I think when I heard this? It was "Holy crap. How bad is it?" (It was that bad, BTW.)
Don't lie, but don't create issues where they don't exist.