What does the word, “truth-up” mean?

There was the following paragraph in the article titled “Welcome to the post-truth presidency” in Washington Post (December 2).

“As Politico’s Susan Glasser wrote in a sobering assessment of election coverage for the Brookings Institution, “Even fact-checking perhaps the most untruthful candidate of our lifetime didn’t work; the more news outlets did it, the less the facts resonated.” So there is no reason to think Trump is about to suddenly truth-up. Indeed, all signs are to the contrary — most glaringly Trump’s chockfull-of-lies tweet that “I won the popular vote if you deduct the millions of people who voted illegally.”

Though Google Ngram indicates that the word, “truth up” is current even before or since the beginning of the 19th century with its peak of usage in mid-1800s, neither Oxford nor Cambridge online dictionaries carry this word.

Does “truth up” mean to try to be more truthful and show integrity? What does “truth up” mean? Is it a popular word?

The construction 'something up' is informal American usage, typically when encouraging, exhorting, or castigating someone. Originally seen in "man up" or "cowboy up" (Free Dictionary), respectively meaning:

to adopt a sufficiently resolute approach or course of action

to adopt a tough approach or course of action

If I say to someone:

You need to man up and finish your college degree

then I'm encouraging and challenging him to be tougher and to finish his studies.

So by extension, 'truth up' means to be more truthful. The sentence you quoted could be written more formally as:

So there is no reason to think Trump is about to suddenly become more truthful.

EDIT

There's another example, 'lawyer up', which means to get a lawyer involved in a problem.

If your boss has been sexually harassing you, I advise you to lawyer up before you do anything else.

The particle (or adverb) up is a very useful word to indicate

with greater intensity

while down is used to indicate

to a lesser degree, level, or rate

Truth-up means to tell the truth with greater intensity or tell the truth more (one level up) compared with the past. It also could be considered short for take (bring) the truth up a notch. The opposite would be take (bring) the truth down a notch.

It appears that the expression, truth-up is uncommon, Oxford Living Dictionaries doesn't contain any mention in its truth entry. The coined expression is really a clever play on words. Consider the ‘satirical’ title of the Washington Post ‘Welcome to the post-truth presidency’, it is evident that truth-up mirrors the word-of-the-year: post-truth. It also echoes the far more common and informal term fess up; (confess; own up) which @PeterPoint in the comments correctly pointed out. _{^{(I've been waiting months to pull off that pun)}}

As @John Feltz explained in his answer, it means to be more truthful but I'll also add the following observation; it is almost demanding or wresting from the President elect, the truth.

Context
The President elect has been accused of telling untruths throughout his presidential campaign; however, despite normal expectations, the hour of reckoning is nowhere in sight.