Again, I submit that it has nothing to do with strategy. I feel that this happens when a city in question has built the improvements allowed by its current technology and there are no wonders available. If it has a nice quota of units, then it likely decides that "it's time to build an improvement" at which time it looks at the list of possibilities. If there is only a palace as a choice, well it starts one of those. Again, not to move its base for any strategic reason, but because it sees the palace as a buildable improvement and just starts it. Of course, it's usually a city that's early in the city list - they're more likely to have all of the other improvements completed. Could explain why it also ends up moving sometimes BACK to the original capital - that city did not have a palace as a choice for a long time, so it may have completed all of the other improvements within that time as well.
I further submit that if a city does start a palace and, for example, discovers seafaring, then in most cases it will continue the palace rather than switch to a harbor. Not sure if that's 100%.
Of course, I've not done any testing on this. I guess it's possible to start a trash game and wait until a moved capital message is given and then look in on the city in question to see if there were other improvements it may have chosen. Of course, new technology may have been discovered from the time it started, so who knows.
When looking for triggers (which must exist as I have trouble thinking the Civ2 AI actually considers capital placement in regard to maximum effect or military vulnerability. If that were the case then they'd actually build cities that INCLUDE specials rather then missing them by one square), I still think it's an internal one like I mentioned rather than a reactionary one to outside influences.