Lyndall Gordon's marvellous biographies of writers (six so far, including TS Eliot, Mary Wollstonecraft and Charlotte Brontë) benefit from critical insights and close reading, but are tempered, and sometimes fruitfully complicated, by deep feeling for her subjects' human dilemmas. With this second volume of memoir she reveals the person who inspired both her love of literature and her powers of sympathy: her mother. It is not a simple story.

Rhoda Press was a gifted woman, unfulfilled as a Cape Town housewife in the 1930s and 40s, but sustained by poetic dreams and a love of reading. Her first child's name was a tribute to the heroine of Olive Schreiner's veld classic The Story of an African Farm and marked Lyndall as "my mother's creature". Rhoda longed for a soulmate, a sister, someone with whom to share her favourite authors: Emily Dickinson, Emily Brontë, William Wordsworth. She read Thomas Mann aloud to her child. Her own poems, too.

But life was made more difficult by an illness that remained mysterious for years – to her daughter at any rate. Gordon opens her book with a dramatic reconstruction of what she had to do, as a four-year-old, when her mother called for help – throw water in her face and press a hairbrush into her wrists as hard as possible. Unsurprisingly, the tiny carer never managed to do this hard enough; Rhoda "wrenches the brush from my hand and drives the bristles back and forth – until she comes round".

From the notebooks, letters and diaries that Gordon inherited when her mother died 15 years ago, it is clear that Rhoda saw her condition (epilepsy, not madness as the child feared) as a creative portal: "Through epilepsy I was stripped down to the foundation rock from which I was able to strike new sparks. For on the edge of that precipice, any weakness in thought, word or deed could plunge one into the bottomless pit, there where all vanities and falsities are expunged." Gordon connects this with the visionary leaps of Dostoevsky's epileptic Myshkin, Wordsworth's "sense sublime" and Emily Brontë's otherworldliness. The biographical bombshell when Gordon wrote about Emily Dickinson in 2012 was to suggest that the poet had been epileptic: now we see where this "flash" of her own came from.

For all its difficulties, Rhoda's was a strange and exciting presence – like a character in a novel. The state of expectancy she lived in made her always on the brink of falling in love, whether it was with a book, a picture, place or person. One of these coups de foudre happened in 1952, four years after her diagnosis, when Rhoda, travelling in Finland with her husband, made an instant connection with a woman at a museum that led to a soul-baring friendship. Their letters are immediately lover-like… "My dear, dear Near-One … it is after all a surprising present to get you thus, although from the first flash of the intuitive contact with you I know what you are." Poems were written, books shared, and, under the influence of this ardent friend, Rhoda decided it was time to give her muse a chance and moved to London, alone, for several years.

Another swerve happened in the mid-1950s, when the Israeli politician Nahum Levin arrived in Cape Town on a Hebrew language promotional mission and, despite needing an interpreter, formed a close liaison with Rhoda. Lyndall, who had got swept up in the general enthusiasm for the fledging state of Israel and embraced "folk-dancing and socialism" in the local Jewish youth movement, accompanied her mother willingly on a trip to Tel Aviv, not realising that Rhoda had her own motives. Lyndall believed that the date she found on her first night was all part of the miraculousness of the promised land, but later discovered that her mother had arranged it in order to have free time with her lover. Lyndall had seen Levin "coming like a comet through the crowd" in the hotel lobby and not understood he was on the way to an assignation. At moments like these, the memoir seems as racy as a novel.

Gordon stayed in Israel with a view to studying and perhaps emigrating there, but disappointed her mother enormously by coming home after a year, inadequately rapturous. Rhoda was glad to have her "sister" back though, and signed up as a student of English literature with her at Cape Town University, telling her Finnish confidante: "I no longer walk by myself and wave my wild tail but live pleasantly in the warm company of L & her friends." It was far from relaxing for Lyndall, though, to be thrust back into the caring role, driving mother to and from classes and helping her find books, "never unaware how a dispirited mood can jump the barriers to an attack. If she's precarious in the morning before we leave or jittery over an essay, I worry."

The unspoken tensions mount as Gordon's narrative moves rapidly from college to marriage to emigration (connected with her husband's career in medicine in New York) to pregnancy, motherhood and breakdown. Suddenly, the promising young postgrad is facing the prospect of being institutionalised forever. This shocking episode – far worse than anything her mother had to endure – draws out a harsher, terser voice and acute analysis (of the treatment she received, in particular) that is rarely unleashed elsewhere.

Towards her mother, though, Gordon seems endlessly generous and grateful, crediting her, for instance, with a way of reading TS Eliot against the critical consensus and vehemently defending her right to fight off "the dark night of depletion" that she thinks motherhood and home life can mean to sensitive women. Gordon insists that she and her brother understood their mother's longings and did not feel deprived when they were left for years in Cape Town with their father (a charming-sounding lawyer and competitive swimmer, whose personality is almost entirely blotted out by his wife's). The reader will almost certainly form a different view. One feels that as a scrupulous biographer, Gordon has laid out all the evidence, but as a memoirist draws back from the conclusions it would be too undaughterly to articulate.

She remains free to celebrate the non-mother, the dreamer, whose letters and notebooks are powerfully eloquent. "Things, meanings, take time to sink into me – only long afterwards when I uncover the reality I am sad to find that my response missed the need," Rhoda told her daughter in 1968. This book realigns those meanings. Literature is where their relationship blossomed and where it is now preserved.

One of Rhoda's notebooks tells how she left her luggage on a bus in Finland and tried to catch up with it courtesy of a passing motorcyclist: "Away I fly. Hair streaming, clutching the shoulders of an unknown man. I have never even seen his face. I don't know where my legs are, and I don't seem to care about them. I am fine, loving it – and laughing, but laughing!"

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