There is no injunction against using EMDR when the eliciting experience is unknown as long as (a) the clinician has completed training (and can use the cognitive interweave), (b) has given appropriate information to the client regarding the fallibiity of memory, and (c) has assessed client readiness.
The purpose of EMDR is not to search out memories, but rather enhance and empower the client in the present. Therefore, any present disturbance can be an appropriate target. The standard protocol suggests targeting (a) past events that have set the foundation for the pathology, (b) current triggers, (c) templates for appropriate future action.
It is best to target known events during early stages of treatment. This is particularly important with complex cases in that it allows the appropriate clinical containment. In addition, for all clients, it is easier to hurry along processing with the cognitive interweave if the event is historically past. Kinesthetic disturbance can be a target if there is no visual imagery, but appropriate judgments need to be made regarding client stability and preparation.