Personally, I think he is making a mistake. As an ordained bishop, he took a vow of obedience.
In my opinion, he would be a better witness to the faith by acceeding to Papal Authority with humility, acknowleging his vow of Holy Obedince and trusting in God and His justice.
St Pio of Pietrelcina was prevented from saying Mass in public and other sanctions from his bishop. He was victim to terrible lies and slander. However, he was obedient to his bishop, even though he’d done nothing to warrant censure. The truth came out after his death, confirming his piety.
This is a frustrating time for believers. However, regardless of who sits in the chair of Peter, the truths of the Church remain immutable.
Paul in Galatians 2:11–13 says: When Peter came to Antioch, I opposed him to his face, because he was clearly in the wrong.
No need to persist in the vow of obedience to those who have abandoned the Catholic faith and essentially renounced it.
You don’t submit to authority of heretics!