Sometimes Donald Trump portrays his election rival, Joe Biden, as a sleepy geriatric who should be in a care home because “he doesn’t know he’s alive”. At others, the president speaks of Biden as a wily manipulator who conspired with the deep state and China.

But in this scattergun approach, the US president has been uncharacteristically reluctant to use what, in normal times, would seem standard political ammunition: an allegation of sexual assault.

It took more than a month after Tara Reade, a former Senate staffer, alleged on a podcast that Biden sexually assaulted her in a Capitol Hill basement in 1993, for Trump to publicly address the matter.

Even then, the US president’s comments on 30 April were unusually milquetoast. “I don’t know anything about it,” Trump said. “I don’t know exactly – I think he should respond. You know, it could be false accusations. I know all about false accusations. I’ve been falsely charged numerous times. And there is such a thing.”

Then, speaking on Fox News’s Fox & Friends, usually a comfort zone, he again declined to go for Biden’s jugular. “Look, he’s got to fight that battle,” he said. “I’ve had battles, too, where I’ve had false accusations, many times. I’ve had many false accusations made, I can tell you that. Many. And maybe it is a false accusation. Frankly, I hope it is, for his sake.”

The first and most obvious explanation for the president’s reticence is that he himself has been accused of assault and unwanted touching by a long list of women, some far more recently than Reade’s account. He also denies the allegations. On the other hand, Trump has never allowed perceived double standards to get in the way of his scorched earth tactics in the past.

Monika McDermott, a political science professor at Fordham University in New York, said: “It’s surprising in a way because usually Trump doesn’t pull back on things even when they do seem hypocritical or ironic or choose your adjective. Yet he is in this particular instance. I don’t know if he’s waiting for something to happen or whether he’s waiting to see how it plays out before he does anything. He seems to be finding what seem to him more fruitful attack routes against Obama and other things and people than against Biden right now.”

In 2016 Trump’s campaign was rocked by the release of an Access Hollywood tape in which he could heard bragging about using his fame to grab women’s private parts. Instead of quitting, he went on the offensive against his rival Hillary Clinton by highlighting sexual assault allegations against her husband, former president Bill Clinton, and even inviting those accusers to a press conference before a presidential debate.

But this November will witness the first presidential election since the rise of the #MeToo movement, which has encouraged women to come forward with allegations of sexual assault against prominent men in politics, show business and other industries.

Biden has committed to picking a woman as his running mate and frequently cites his work as lead sponsor of the Violence Against Women Act. Both candidates are keenly aware that suburban women could be a pivotal demographic in the final vote.

While Trump remains taciturn, Republicans have instead focused much of their response on Brett Kavanaugh, the supreme court justice whose nomination was nearly derailed by sexual misconduct allegations. The Trump campaign pointed to statements made by Democrats during the Kavanaugh episode to portray them as hypocritical.

Erin Perrine, principal deputy communications director at the Trump campaign, said: “During Justice Kavanaugh’s hearings, Biden made clear that all women should be believed when they come forward with allegations of sexual assault. Biden’s own work during the Obama administration lowered standards for such accusations on college campuses as to effectively institute a presumption of guilt. In a dramatic shift, Biden now says ‘believe women’ doesn’t actually mean ‘believe women.’”

Trump himself, however, has preferred to take aim at other targets, seeking to implicate Biden in a so-called “Obamagate” conspiracy that many seen as an attempt to deflect attention from the coronavirus pandemic – likely to prove a more significant issue in November.

Amid Democratic alarm that the Reade allegation could dent Biden’s support among women, the former vice-president vehemently denied it in an interview on the MSNBC network on 1 May and repeated that position in a series of media appearances.

The story has faded from prominence in recent days, especially after the PBS NewsHour interviewed 74 former Biden staffers, of whom 62 were women, and found none said that they had experienced sexual harassment, assault or misconduct by Biden, nor ever heard rumors or allegations to that effect.

By pushing the case, Trump may have more to lose than to gain. Rich Galen, a former Republican strategist, said: “The case against Biden keeps getting thinner and thinner so I’m not sure that there’s much there. And all the people who’s accused Trump, it would be like listing the names of the people who died in Vietnam every night.”

Michael Steele, former chairman of the Republican National Committee, added: “Trump, if nothing else, knows how to read his audience: ‘No, they’re not going to buy anything I sell on this point.’ There’s no need to even open that Pandora’s box because it’s a Pandora’s box for him, not Joe Biden. I think that’s why the president has largely decided not to engage at that level.

“My sense is right now, despite what others in the campaign may want to do, there is no energy from the president himself to open up that door and go through it.”