I think contacting Quayle made perfect sense as he is the only living Republican VP to take part in what he was about to take part in - certifying your own defeat.Pence asked Dan Quale for advice on whether or not he, as Vice President, has the power to end democracy in the USA. This tells me that Pence targeted an idiot like Dan Quale, hoping that his best advice would be to go ahead and end democracy, thus telling everyone else that Dan Quale told him to do it.
Trump had already called for his mob to take out Pence, his own VP. and Pence still walked back in to the top of the fellatio line in front of Trump after the insurrection, anyway.
You can't trust the empty husk of human flesh that is Mike Pence.
Pence did the right thing in the face of enormous pressure.