If you mean something where what it says is static, but the color of the text changes seasonally (like family name, street address, or a general welcome sign), you could do it more easily with a wooden sign cut clear through, and then colored acrylic back panels.
If the whole sign changes, then two tone acrylic and a full swap out of signs is pretty easy, though that pulls back from the nice hardwood.
Unless you mean a free floating sign that would be seen from both sides… then emulating the approach used for the flag is indeed the only way to go.
I’ve done some acrylic LED signs using programmable color changes with LED strips (like this: Amazon.com) which have a little remote control to change the color (or let it cycle). They’re showing unavailable now but Amazon shows a lot of other similar ones. They have 4 strips of lights (which can be daisy chained or cut to length as desired). Mounted in the bottom (or top) of an aluminum channel frame and wired into a 5VDC power supply. These came with USB connections but are easy to clip and wire to batteries or a power supply. For a house sign, it would be pretty easy to build all of that into a wood or acrylic bottom frame of the sign with a switch and a light sensor inline so it only turns on when it’s dark.