There are connections between Q and the Secret Space Program in. Its existence was acknowledged in Q2225. A person who patented what essentially looks like a TR-3B (https://patents.google.com/patent/US20060145019A1/en) goes by the name "St Clair John Q".
Seeing that GEOTUS created the Space Force, which is according to some people an attempt to transfer Secret Space Program/Solar Warden assets into the public domain and begin declassifying the technologies, is it too far-fetched to say that the President is currently staying on a classified space ship or station?
What could be some connections between CASTLE_ROCK and other (endgame-related) drops, the SSP/Solar Warden, NASA, astronauts and space and astronomy in general?
Well, considering the joint military base he went to, he might now be on a nuclear sub. That would be a much less extreme alternative (and very safe).
I guess we should just admit that we have no idea where he is. He may have done a short phone interview recently when he endorsed someone for the head of AZ GOP or something like that...