In short, that would make Tokuhon an uncle of Naokatsu NAGAI (son of Shigemoto who changed his surname), who in turn was a close confident of Hidetada (castle guard) who became seriously ill as mentioned above.
つまり先述の秀忠重病時の秀忠側近（書院番）であった永井直勝（重元の息子。改姓）の叔父に当たる。