In January 2020, the rightwing Arkansas Republican Tom Cotton said he would vote to acquit Donald Trump in his first impeachment trial because despite senators having “heard from 17 witnesses … and received more than 28,000 pages of documents”, Democrats had not presented their case correctly.

According to Cotton, the senators who sat through so much evidence would “perform the role intended for us by the founders, of providing the ‘cool and deliberate sense of the community’, as it says in Federalist 63.”

In a new book, however, Cotton boasts that he spent his time refusing to pay attention – pretending to read materials relevant to the president’s trial – but hiding his real reading matter under a fake cover.

He writes: “My aides delivered a steady flow of papers and photocopied books, hidden underneath a fancy cover sheet labeled ‘Supplementary Impeachment Materials’, so nosy reporters sitting above us in the Senate gallery couldn’t see what I was reading.”

“They probably would’ve reported that I wasn’t paying attention to the trial.”

Reporters did report that Republicans were not paying attention. Marsha Blackburn of Tennessee named the book she chose to read instead of participating in only the third presidential trial in history: “It was Resistance (At All Costs) by Kim Strassel.”

Other Republicans fidgeted or doodled. But reporters noted that Blackburn violated decorum guidelines on relevant reading: “Reading materials should be confined to only those readings which pertain to the matter before the Senate.”

Admitting the same infraction, Cotton – a leading China hawk – says he was reading “about the science of coronaviruses, the methods of vaccine development and the history of pandemics”.

He adds: “I was paying attention – to the story that mattered most. The outcome of the impeachment trial was a foregone conclusion, and it wouldn’t impact the daily lives of normal Americans.”

Cotton’s book, Only the Strong: Reversing the Left’s Plot to Sabotage American Power, will be published next Tuesday. The Guardian obtained a copy.

Cotton is now among senators, governors and former members of the Trump administration jostling for position in the developing contest for the Republican presidential nomination in 2024. Publishing a book is a traditional preparatory step.

The senator, 45, is a former soldier who served in Iraq and Afghanistan and at Arlington Cemetery before entering politics as a foreign policy hawk. His book takes aim at Joe Biden and Barack Obama – and equally persistently, from the prologue to the note on sources, Woodrow Wilson, the president who took office in 1913, took the US into the first world war in 1917, left office in 1921 and died in 1924.

Trump is the clear frontrunner for the Republican nomination 100 years later, despite facing legal jeopardy for inciting the Capitol attack, trying to overturn the 2020 election, retaining classified records and being the subject of criminal and civil suits over his business affairs and an allegation of rape.

Cotton voted to acquit Trump at both his impeachment trials, the second for inciting the Capitol riot, but he was not among the eight Republican senators who supported Trump’s attempts to overturn election results in key states.

In his book, however, the Arkansan skips over domestic concerns, including his own advocacy of using the military against “Antifa terrorists” during protests for racial justice in summer 2020, a position which stoked huge controversy and brought down an editor at the New York Times.

Cotton is largely careful to target only Democratic presidents. Hitting Bill Clinton and Barack Obama for not serving in the military before running for the White House, he omits mention of George W Bush’s avoidance of service in Vietnam by securing a post in the Texas air national guard, to which he did not always show up.

But Cotton does risk angering Trump, by criticising him for “waiting too long to withdraw from the Iran nuclear deal” and by dishing on a private call in which the then president professed ignorance of military protocol.

Early in Trump’s term in power, Cotton writes, the president called him about a potential nominee – common Senate business.

But Trump then said: “The other night, they called me and asked for approval to kill some terrorist. I never heard of the guy.”

Cotton asked if Trump approved the strike.

“Trump replied, ‘Oh yeah, but I asked why they called me in the first place. Didn’t they have some captain or major or someone who knew more about this guy? I mean, I’d never heard of him.’”

With nudging, Cotton says, Trump worked out that the military was working according to protocols laid down by Obama, who he accuses of “impos[ing] needless layers of bureaucratic and legal review” on strikes on terrorist targets.