The Siamese twin character is actually a product of a mad scientist sewing two halves of separate female bodies together and keeping both heads.

Their body will essentially look like one body apart from widening up towards the shoulders to fit the two heads with a little space between both necks and heads.

Ignoring the realities that this wouldn't be likely possible in the real world how can I at times get away with them going out in public maybe taking turns to be in control with the other head quietly hides somehow?

As they are female there may be more options for extravagant clothing and head garments or if theres another options that can allow this character to hide the second head for short moments out in public other than maybe turning to the side or other obscuring view points.

Edit, I just thought a strange haircut could be an option, the hiding one pushing the hair over their face as the other combs some of theres over the hidden head but I am not sold on this idea yet.