At last week’s presidential debate, Donald Trump said (albeit through gritted teeth) that the thing he most admired about his opponent, Hillary Clinton, was that she never gives up. She’s got stamina. She’s on the cusp of succeeding at the one thing she’s wanted for decades, and she’s not going to quit at the final hurdle.

Determination of this order, an inner grit and resilience, is a state of being admired by many Americans, fetishised as it is by the myth of the “American Dream”. If you want something enough, and you work hard enough, it can be yours – even, or especially, the presidency.

This is exactly the sort of characteristic that might, in the eleventh hour, push a swing voter in Hillary’s direction. Trump knows that and, having openly highlighted her strengths, he needed to do something to compensate. His call for both candidates to take a drugs test, and his insinuation that her strength and prowess during the latest gruelling live TV debate was down to the use of medicinals – despite any evidence to that end – is clever indeed.

Nigel Farage compares Donald Trump to a silverback gorilla in the second presidential debate

By suggesting that Hillary is either unwell or requiring medical treatment to participate in the campaign trail, Trump is tapping into a latent misogyny that runs deep in American and British society – the persistent idea that women are not physiologically cut out for the tough stuff.

This is the oldest form of sexism in the book. From the claim that the “wandering womb” could turn women hysterical to the modern idea that hormones exert complete control over women’s lives; from the consumptive and swooning heroines of early modern fiction to the spurious claims that men and women’s brains are wired in fundamentally different ways; from tabloid newspapers and glossy magazines reporting research (conducted, dubiously, by luxury “wellness” brands) that “80 per cent of women are pushing themselves too hard”, to this latest claim from Trump (without any supporting evidence) that Clinton was so exhausted after the presidential debate that she could “barely reach her car”, the idea that women are physically unsuited to exert power or leadership – utter nonsense though that is – has been with us since time immemorial.

Bookmakers are offering odds of 25/1 on Clinton failing the test Trump is demanding they both take. After recent revelations over his comments about women, one might not so much as raise an eyebrow hair even if “The Donald” came right out and said that he believed his rival was not physically or psychologically prepared for office because of her gender. But, given that would, in more normal circumstances, be the kind of outburst that would rule a presidential candidate out of the running, his comments here about drug testing insinuate that view without needing to state it explicitly. He’s tapping into a commonly-held if not often outwardly expressed view that there are still some jobs, some responsibilities, that are just too much for a woman to handle.

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Hillary’s biggest handicap in this presidential race is not those leaked emails, or her husband’s indiscretions, but the simple fact of her being a female. Is America ready for a “First Gentleman”?