I think independents are exactly what the name implies - Independent! They might have druthers but they are not, I think, dedicated to one party or the other. Perhaps they are voting for the candidate and screw the party? I really have no idea and, I suspect, neither does anybody else.
I consider myself, for instance, an independent. I also tend toward the left a bit but am not really dedicated to that direction when the candidate on that side is utterly wrong (for me). Sometimes I might even vote for nobody in a given position if they are both rotters.
I have, incidentally, never voted in an elections wherein you are forced to vote for a given party if you are signed up in that party but I think there are instances where that actually happens. I am in Washington state and we get to vote for whoever we want. We also decide who gets to run in the run-off by determining who the two top vote getters in the primary were. This sometimes means that both candidates, in the runoff, might actually be running in the same election! (this one has amused more often than not)