Impeachment is a bit different than a standard criminal proceeding. However, I will proceed as if the provisions and protections of the Fifth Amendment of the U.S. Constitution apply. In other words, IncognitoGuy cannot be compelled to testify against himself. What this means going forward: IncognitoGuy may choose to simply invoke the Fifth Amendment to block his deposition. However, if he does so, then he must remain silent throughout the remaining proceedings. (Accused criminal defendants are allowed to remain silent at their trials, but if they speak in their own favor then they automatically become subject to cross-examination.)