The main symptom of separation anxiety is a refusal to leave the parent. It may take the form in the younger child of actively physically clinging to the parent (hanging out of the mother's skirt) or of resisting separation from the parent by other means.
Children who are fearful of change often do not let parents out of their sight. For example, it is not uncommon for children if they lose one parent to become excessively clingy towards the remaining parent. Fear of loss motivates this behaviour. Children who understand some of what has been happening in the US and who have ingested the distress of their parents may well become fearful and exhibit certain classic symptoms.
Young children may physically cling more, refuse to let parents "out of their sight" and seek excessive proximity to parents and home.
Older children may refuse to go to school. An older child may exhibit their fear by complaining of feeling sick. This is one way to stay at home and "keep an eye on a parent".
Children who are afraid that in their absence a parent might disappear often unconsciously find ways of keeping parents nearby.
This can take the form of attention-seeking behaviour, somatic complaints or refusal to engage in previously enjoyed independent activities.
There may be excessive questioning of parents about where they are going, what they are doing, when they will be home, how they can be contacted.
These questions need to be answered patiently and calmly.